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Journal articles on the topic 'K-graph system'

Author: Grafiati

Published: 25 May 2024

Last updated: 31 July 2025

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1

Asif, Muhammad, Hamad Almohamedh, Muhammad Hussain, Khalid M. Alhamed, Abdulrazaq A. Almutairi, and Sultan Almotairi. "An Approach to the Geometric-Arithmetic Index for Graphs under Transformations’ Fact over Pendent Paths." Complexity 2021 (June 24, 2021): 1–13. http://dx.doi.org/10.1155/2021/3745862.

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Graph theory is a dynamic tool for designing and modeling of an interconnection system by a graph. The vertices of such graph are processor nodes and edges are the connections between these processors nodes. The topology of a system decides its best use. Geometric-arithmetic index is one of the most studied graph invariant to characterize the topological aspects of underlying interconnection networks or graphs. Transformation over graph is also an important tool to define new network of their own choice in computer science. In this work, we discuss transformed family of graphs. Let Γ n k , l b

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Il’ev, A. V., and V. P. Il’ev. "ALGORITHMS FOR SOLVING SYSTEMS OF EQUATIONS OVER VARIOUS CLASSES OF FINITE GRAPHS." Prikladnaya Diskretnaya Matematika, no. 53 (2021): 89–102. http://dx.doi.org/10.17223/20710410/53/6.

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The aim of the paper is to study and to solve finite systems of equations over finite undirected graphs. Equations over graphs are atomic formulas of the language L consisting of the set of constants (graph vertices), the binary vertex adjacency predicate and the equality predicate. It is proved that the problem of checking compatibility of a system of equations S with k variables over an arbitrary simple n-vertex graph Γ is N P-complete. The computational complexity of the procedure for checking compatibility of a system of equations S over a simple graph Γ and the procedure for finding a gen

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RANAWAKE, U. A., P. M. LENDERS, and S. M. GOODNICK. "ON LOWER BOUNDS FOR THE COMMUNICATION VOLUME IN DISTRIBUTED SYSTEMS." Parallel Processing Letters 01, no. 02 (1991): 125–33. http://dx.doi.org/10.1142/s0129626491000070.

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In this paper we derive a lower bound for the total communication volume when mapping arbitrary task graphs onto a distributed processor system. For a K processor system this lower bound can be computed with only the K (possibly) largest eigen values of the adjacency matrix of the task graph and the eigen values of the adjacency matrix of the processor graph. We also derive the eigen values of the adjacency matrix of the processor graph for a hypercube multiprocessor and illustrate the concept with a simple example for the two processor case.

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Hong, Yanmei, Yihong Wu, and Qinghai Liu. "Redundant Trees in Bipartite Graphs." Mathematics 13, no. 6 (2025): 1005. https://doi.org/10.3390/math13061005.

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It has been conjectured that for each positive integer k and each tree T with bipartite (Z1,Z2), every k-connected bipartite graph G with δ(G)≥k+max{|Z1|,|Z2|} admits a subgraph T′≅T such that G−V(T′) is still k-connected. In this paper, we generalize the ear decompositions of 2-connected graphs into a (k,ak)-extensible system for a general k-connected graph. As a result, we confirm the conjecture for k≤3 by proving a slightly stronger version of it.

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Ustimenko, Vasyl O., and Oleksandr S. Pustovit. "On security of GIS systems with N-tier architecture and family of graph based ciphers." Environmental safety and natural resources 47, no. 3 (2023): 113–32. http://dx.doi.org/10.32347/2411-4049.2023.3.113-132.

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Discovery of q-regular tree description in terms of an infinite system of quadratic equations over finite field Fq had an impact on Computer Science, theory of graph based cryptographic algorithms in particular. It stimulates the development of new graph based stream ciphers. It turns out that such encryption instruments can be efficiently used in GIS protection systems which use N-Tier Architecture. We observe known encryption algorithms based on the approximations of regular tree, their modifications defined over arithmetical rings and implementations of these ciphers. Additionally new more

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Chen, Haiyan, and Fuji Zhang. "Spectral Dynamics of Graph Sequences Generated by Subdivision and Triangle Extension." Electronic Journal of Linear Algebra 32 (February 6, 2017): 454–63. http://dx.doi.org/10.13001/1081-3810.3583.

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For a graph G and a unary graph operation X, there is a graph sequence \G_k generated by G_0=G and G_{k+1}=X(G_k). Let Sp({G_k}) denote the set of normalized Laplacian eigenvalues of G_k. The set of limit points of \bigcup_{k=0}^\infty Sp(G_k)$, $\liminf_{k\rightarrow\infty}Sp(G_k) and $\limsup_{k\rightarrow \infty}Sp(G_k)$ are considered in this paper for graph sequences generated by two operations: subdivision and triangle extension. It is obtained that the spectral dynamic of graph sequence generated by subdivision is determined by a quadratic function, which is closely related to the the w

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Ngo, Tien, Jiao Yin, Yong-Feng Ge, and Hua Wang. "Optimizing IoT Intrusion Detection—A Graph Neural Network Approach with Attribute-Based Graph Construction." Information 16, no. 6 (2025): 499. https://doi.org/10.3390/info16060499.

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The inherent complexity and heterogeneity of the Internet of Things (IoT) ecosystem present significant challenges for developing effective intrusion detection systems. While graph deep-learning-based methods have shown promise in cybersecurity applications, existing approaches primarily construct graphs based on physical network connections, which may not effectively capture node representations. This paper proposes a Top-K Similarity Graph Framework (TKSGF) for IoT network intrusion detection. Instead of relying on physical links, the TKSGF constructs graphs based on Top-K attribute similari

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Shirdel, G. H., M. Ghanbari, and M. Ramezani. "Generalized 3-Rainbow Domination in Graphs and Honeycomb System (HC(n))." Utilitas Mathematica 119, no. 1 (2024): 3–7. http://dx.doi.org/10.61091/um119-01.

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In this paper, we introduce the concept of the generalized 3 -rainbow dominating function of a graph G . This function assigns an arbitrary subset of three colors to each vertex of the graph with the condition that every vertex (including its neighbors) must have access to all three colors within its closed neighborhood. The minimum sum of assigned colors over all vertices of G is defined as the g 3 -rainbow domination number, denoted by γ g 3 r . We present a linear-time algorithm to determine a minimum generalized 3-rainbow dominating set for several graph classes: trees, paths ( P n ) , cyc

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Razumovsky, P. V., and M. B. Abrosimov. "THE MINIMAL VERTEX EXTENSIONS FOR COLORED COMPLETE GRAPHS." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 13, no. 4 (2021): 77–89. http://dx.doi.org/10.14529/mmph210409.

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The article proposes the results of the search for minimal vertex extensions of undirected colored complete graphs. The research topic is related to the modelling of full fault tolerant technical systems with a different type of their objects in the terminology of graph theory. Let a technical system be Σ, then there is a graph G(Σ), which vertices reflects system’s objects and edges reflects connections between these objects. Type of each object reflected in a mapping of some color from F = {1,2…,i} to the corresponding vertex. System’s Σ vertex extension is a graph G(Σ) which contains additi

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Lobov, Alexander A., and Mikhail B. Abrosimov. "About uniqueness of the minimal 1-edge extension of hypercube Q4." Prikladnaya Diskretnaya Matematika, no. 58 (2023): 84–93. http://dx.doi.org/10.17223/20710410/58/8.

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One of the important properties of reliable computing systems is their fault tolerance. To study fault tolerance, you can use the apparatus of graph theory. Minimal edge extensions of a graph are considered, which are a model for studying the failure of links in a computing system. A graph G* = (V*,α*) with n vertices is called a minimal k-edge extension of an n-vertex graph G = (V, α) if the graph G is embedded in every graph obtained from G* by deleting any of its k edges and has the minimum possible number of edges. The hypercube Qn is a regular 2n-vertex graph of order n, which is the Cart

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Pavlopoulou, Niki. "Dynamic Diverse Summarisation in Heterogeneous Graph Streams: a Comparison between Thesaurus/Ontology-based and Embeddings-based Approaches." International Journal of Graph Computing 1, no. 1 (2020): 70–94. http://dx.doi.org/10.35708/gc1868-126724.

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Nowadays, there is a lot of attention drawn in smart environments, like Smart Cities and Internet of Things. These environments generate data streams that could be represented as graphs, which can be analysed in real-time to satisfy user or application needs. The challenges involved in these environments, ranging from the dynamism, heterogeneity, continuity, and high-volume of these real-world graph streams create new requirements for graph processing algorithms. We propose a dynamic graph stream summarisation system with the use of embeddings that provides expressive graphs while ensuring hig

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Aslam, Adnan, Safyan Ahmad, Muhammad Ahsan Binyamin, and Wei Gao. "Calculating topological indices of certain OTIS interconnection networks." Open Chemistry 17, no. 1 (2019): 220–28. http://dx.doi.org/10.1515/chem-2019-0029.

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AbstractRecently, increasing attention has been paid to The Optical Transpose Interconnection System (OTIS) network because of its prospective applications in architectures for parallel as well as distributed systems [27, 28]. Different interconnection networks in the context of topological indices are researched recently in [25, 26]. This article includes the computions of the general Randi´c, first and second Zagreb, general sum connectivity, first and second multiple zagreb, hyper zagreb, ABC and GA indices for OTIS (swapped and biswapped) networks by taking path and k-regular graph on n ve

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Ionescu, Marius, and Yasuo Watatani. "C*-Algebras Associated with Mauldin–Williams Graphs." Canadian Mathematical Bulletin 51, no. 4 (2008): 545–60. http://dx.doi.org/10.4153/cmb-2008-054-0.

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AbstractA Mauldin–Williams graph is a generalization of an iterated function system by a directed graph. Its invariant set K plays the role of the self-similar set. We associate a C*-algebra (K) with a Mauldin–Williams graph and the invariant set K, laying emphasis on the singular points. We assume that the underlying graph G has no sinks and no sources. If satisfies the open set condition in K, and G is irreducible and is not a cyclic permutation, then the associated C*-algebra (K) is simple and purely infinite. We calculate the K-groups for some examples including the inflation rule of the P

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Romankevich, Vitaliy A., Ihor A. Yermolenko, Kostiantyn V. Morozov, and Alexei M. Romankevich. "Graph-logical models for (n, f, k) – and consecutive - k-out-of-n – systems." Herald of Advanced Information Technology 7, no. 3 (2024): 296–308. http://dx.doi.org/10.15276/hait.07.2024.21.

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The article is devoted to methods of constructing graph-logical models of fault-tolerant multiprocessor systems. In particular, systems of the type (n, f, k), linear consecutive-k-out-of-n and circular consecutive-k-out-of-n are considered, which are characterized by the failure of the system when a certain number of consecutive processors fail. Graph-logical models can be used to estimate the reliability parameters of fault-tolerant multiprocessor systems by conducting statistical experiments with models of their behavior in the failure flow. The graph-logical models under construction are ba

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Mirakyan, Martin. "ABCDE: Approximating Betweenness-Centrality ranking with progressive-DropEdge." PeerJ Computer Science 7 (September 6, 2021): e699. http://dx.doi.org/10.7717/peerj-cs.699.

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Betweenness-centrality is a popular measure in network analysis that aims to describe the importance of nodes in a graph. It accounts for the fraction of shortest paths passing through that node and is a key measure in many applications including community detection and network dismantling. The computation of betweenness-centrality for each node in a graph requires an excessive amount of computing power, especially for large graphs. On the other hand, in many applications, the main interest lies in finding the top-k most important nodes in the graph. Therefore, several approximation algorithms

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SOBOLEVA, E. "VASSILIEV KNOT INVARIANTS COMING FROM LIE ALGEBRAS AND 4-INVARIANTS." Journal of Knot Theory and Its Ramifications 10, no. 01 (2001): 161–69. http://dx.doi.org/10.1142/s0218216501000809.

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We study the 4-bialgebra of graphs and the bialgebra of 4-invariants introduced by S. K. Lando. Our main goal is the investigation of the relationship between 4-invariants of graphs and weight systems arising in the theory of finite order invariants of knots. In particular, we show that the corank of the adjacency matrix of a graph leads to the weight system coming from the defining representation of the Lie algebra gl(N).

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Panić, Biljana, Nataša Kontrec, Mirko Vujošević, and Stefan Panić. "A Novel Approach for Determination of Reliability of Covering a Node from K Nodes." Symmetry 12, no. 9 (2020): 1461. http://dx.doi.org/10.3390/sym12091461.

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In this paper, a stochastic problem of multicenter location on a graph was formulated through the modification of the existing p-center problem to determine the location of a given number of facilities, to maximize the reliability of supplying the system. The system is represented by a graph whose nodes are the locations of demand and the potential facilities, while the weights of the arcs represent the reliability, i.e., the probability that an appropriate branch is available. First, k locations of facilities are randomly determined. Using a modified Dijkstra’s algorithm, the elementary path

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Wang, Shiying, and Yunxia Ren. "g-Good-Neighbor Diagnosability of Arrangement Graphs under the PMC Model and MM* Model." Information 9, no. 11 (2018): 275. http://dx.doi.org/10.3390/info9110275.

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Diagnosability of a multiprocessor system is an important research topic. The system and interconnection network has a underlying topology, which usually presented by a graph G = ( V , E ) . In 2012, a measurement for fault tolerance of the graph was proposed by Peng et al. This measurement is called the g-good-neighbor diagnosability that restrains every fault-free node to contain at least g fault-free neighbors. Under the PMC model, to diagnose the system, two adjacent nodes in G are can perform tests on each other. Under the MM model, to diagnose the system, a node sends the same task to tw

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Ali, Muhammad Ali Rushdi, and Mohammad Alturki Alaa. "Computation of k-out-of-n System Reliability via Reduced Ordered Binary Decision Diagrams." British Journal of Mathematics & Computer Science 22, no. 3 (2017): 1–9. https://doi.org/10.9734/BJMCS/2017/33642.

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A prominent reliability model is that of the partially-redundant (k-out-of-n) system. We use algebraic as well as signal-flow-graph methods to explore and expose the AR algorithm for computing k-out-of-n reliability. We demonstrate that the AR algorithm is, in fact, both a recursive and an iterative implementation of the strategy of Reduced Ordered Binary Decision Diagrams (ROBDDs). The underlying ROBDD for the AR recursive algorithm is represented by a compact Signal Flow Graph (SFG) that is used to deduce AR iterative algorithms of quadratic temporal complexity and linear spatial complexity.

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20

Chang, G. J., and F. K. Hwang. "Optimal Consecutive-k−Out−of−n Systems under a Fixed Budget." Probability in the Engineering and Informational Sciences 2, no. 1 (1988): 63–73. http://dx.doi.org/10.1017/s0269964800000632.

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A consecutive-k−out−of−n system is a graph with n vertices where the system fails if and only if some path of k consecutive vertices all fail. The assumption is made that qi, is the failing probability of the ith vertex and the states of the vertices are statistically independent. The problem is to find the best system, i.e., a set {q1, …,qn}, and its assignment to the vertices of the system graph that maximizes the reliability of the system, under the constraint that the product of qi's is a constant. We solve the problem for all lines and some cycles. We then extend our results to trees and

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Huang, Da, Jibin Yang, Xing Chen, and Xiaolin Fan. "On Consensus Indices of Triplex Multiagent Networks Based on Complete k-Partite Graph." Symmetry 14, no. 8 (2022): 1586. http://dx.doi.org/10.3390/sym14081586.

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In this article, the performance indices on consensus problems for three-layered, multiagent systems are studied from the perspective of algebraic graph theory, where the indices can be used as a measurement of the system performance and refer to the network coherence and algebraic connectivity. Specifically, some operations of two graphs are applied to established the three-layered networks based on k-partite structure, and the mathematical expression of the coherence is derived by the methods of algebraic graph theory. We found that the operations of adding star-shaped copies or fan-graph co

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Yao, Y. C. "On Optimal Consecutive k-out-of-n: F Systems Subject to a Fixed Product of Failure Probabilities." Probability in the Engineering and Informational Sciences 3, no. 2 (1989): 165–73. http://dx.doi.org/10.1017/s0269964800001078.

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A consecutive−k−out−of−n:F system is an n−vertex graph where the system fails if and only if some k consecutive vertices all fail. Assuming that the n vertices have, independently, the respective failure probabilities q1,…, qn, the problem is to find, subject to πqi = Q (a constant), a set of q1,…, qn so as to maximize the system reliability. In the case that the graph is a circle (or cycle), Chang and Hwang [1] conjectured that q1 =… = qn, = Q1/n is optimal if n and k are relatively prime. In this paper, it is shown that the conjecture is true for sufficiently small Q. It is also shown by cou

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Vilakone, Phonexay, and Doo-Soon Park. "The Efficiency of a DoParallel Algorithm and an FCA Network Graph Applied to Recommendation System." Applied Sciences 10, no. 8 (2020): 2939. http://dx.doi.org/10.3390/app10082939.

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This article investigates the efficiency of a doParallel algorithm and a formal concept analysis (FCA) network graph applied to recommendation systems. It is the first article using the FCA method to create a network graph and apply this graph to improve the accuracy of a recommendation system. According to the fundamental knowledge about users who have similar feature information, they may like the same items. This idea was used to create an FCA network graph. In the proposed process, the k-clique method was used to divide this network graph into various communities. A combination of the k-ne

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LIU, WENJUN. "The Relationship Between Extra Connectivity and t/k-Diagnosability of Regular Networks." Journal of Interconnection Networks 20, no. 01 (2020): 2050003. http://dx.doi.org/10.1142/s0219265920500036.

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The g-extra connectivity of a multiprocessor system modeled by a graph G, denoted by [Formula: see text] (G), is the minimum number of removed vertices such that the network is disconnected and each residual component has no less than g + 1 vertices. The t/k-diagnosis strategy can detect up to t faulty processors which might include at most k misdiagnosed processors. These two parameters are important to measure the fault tolerant ability of a multiprocessor system. The extra connectivity and t/k-diagnosability of many well-known networks have been investigated extensively and independently. H

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LOERA, J. A., J. LEE, S. MARGULIES, and S. ONN. "Expressing Combinatorial Problems by Systems of Polynomial Equations and Hilbert's Nullstellensatz." Combinatorics, Probability and Computing 18, no. 4 (2009): 551–82. http://dx.doi.org/10.1017/s0963548309009894.

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Systems of polynomial equations over the complex or real numbers can be used to model combinatorial problems. In this way, a combinatorial problem is feasible (e.g., a graph is 3-colourable, Hamiltonian, etc.) if and only if a related system of polynomial equations has a solution.For an infeasible polynomial system, the (complex) Hilbert Nullstellensatz gives a certificate that the associated combinatorial problem is infeasible. Thus, unless P = NP, there must exist an infinite sequence of infeasible instances of each hard combinatorial problem for which the minimum degree of a Hilbert Nullste

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Jiang, Yaozhi. "Dialectical Logic K-Model: A Mathematical Model for Machine." Journal of Mathematics Research 9, no. 6 (2017): 82. http://dx.doi.org/10.5539/jmr.v9n6p82.

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An axiom system for dialectical logic K-model which based on Kirchhoff energy-method is established by author in the paper. The author describes that subjective-laws is the mirror imagine reflected from objective-laws and defines that the three-step which named by sensation, abstraction and thinking in artificial intelligence. At same time, describes that axiom system for dialectical logic K-model, in which contains such as logic-variable energy conservation law, Mozi’s principle( mini-max principle) and forbidden law, etc. In the axiom system also contain such as a continuous true-value-funct

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JENAB, K., and B. S. DHILLON. "k-OUT-OF-n SYSTEM WITH SELF-LOOP UNITS." International Journal of Reliability, Quality and Safety Engineering 12, no. 01 (2005): 61–73. http://dx.doi.org/10.1142/s0218539305001665.

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This paper presents an analytical approach for a k-out-of-n system with units having the failure detection, isolation, and recovery mechanisms. The approach uses the flow-graph concept and moment generating function (MGF) to analyze the reliability of the k-out-of-n system with self-loop units. This newly developed analytical approach provides the probability of system failure, system mean, and standard deviation time to failure. A solved example is presented to demonstrate the application of the approach.

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Zhang, Zhanqi, and Yingqing Xiao. "Graph Concatenations to Derive Weighted Fractal Networks." Complexity 2020 (July 18, 2020): 1–9. http://dx.doi.org/10.1155/2020/4906878.

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Given an initial weighted graph G0, an integer m>1, and m scaling factors f1,…,fm∈0,1, we define a sequence of weighted graphs Gkk=0∞ iteratively. Provided that Gk−1 is given for k≥1, we let Gk−11,…,Gk−1m be m copies of Gk−1, whose weighted edges have been scaled by f1,…,fm, respectively. Then, Gk is constructed by concatenating G0 with all the m copies. The proposed framework shares several properties with fractal sets, and the similarity dimension dfract has a great impact on the topology of the graphs Gk (e.g., node strength distribution). Moreover, the average geodesic distance of Gk in

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Adinayev, Arthur, and Itamar Stein. "Diamond Subgraphs in the Reduction Graph of a One-Rule String Rewriting System." Fundamenta Informaticae 178, no. 3 (2021): 173–85. http://dx.doi.org/10.3233/fi-2021-2002.

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In this paper, we study a certain case of a subgraph isomorphism problem. We consider the Hasse diagram of the lattice Mk (the unique lattice with k + 2 elements and one anti-chain of length k) and find the maximal k for which it is isomorphic to a subgraph of the reduction graph of a given one-rule string rewriting system. We obtain a complete characterization for this problem and show that there is a dichotomy. There are one-rule string rewriting systems for which the maximal such k is 2 and there are cases where there is no maximum. No other intermediate option is possible.

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Krieger, Wolfgang, and Kengo Matsumoto. "A lambda-graph system for the Dyck shift and its $K$-groups." Documenta Mathematica 8 (2003): 79–96. http://dx.doi.org/10.4171/dm/139.

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Gomes, Thiago Eliandro de Oliveira, Vinícius Jacques Garcia, and André Ross Borniatti. "Analysis of Clustering Algorithms Applied to Distribution Network Reconfiguration." Revista de Gestão Social e Ambiental 18, no. 11 (2024): e09905. http://dx.doi.org/10.24857/rgsa.v18n11-166.

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Objective: The study aims to speed up the reconfiguration process of electrical distribution networks. Using graph theory, it explores methods for the network's topological decomposition and searches for lower-cost paths to optimize the distribution network configuration. Related Studies: The research is based on graph theory, which allows modeling the connections of an electrical network as an interconnected graph. Important references include clustering techniques and algorithms for finding minimum paths in graphs, applying methods such as Malgrange, K-means, DBSCAN, SOM, and classical graph

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Sarkar, Dilip, Shridhar Kumar, Pratibhamoy Das, and Higinio Ramos. "Higher-order convergence analysis for interior and boundary layers in a semi-linear reaction-diffusion system networked by a $ k $-star graph with non-smooth source terms." Networks and Heterogeneous Media 19, no. 3 (2024): 1085–115. http://dx.doi.org/10.3934/nhm.2024048.

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<p>We investigated a nonlinear singularly perturbed elliptic reaction-diffusion coupled system having non-smooth data networked by a $ k $-star graph. We considered all possible boundary conditions at the free boundary located at the tail of the edge and imposed the continuity condition with Kirchhoff's junction law at the junction point of the $ k $-star graph to obtain a continuous solution for this coupled system. First, we showed the existence and uniqueness of the solution using the variational formulation approach. Then, we reformulated it into a minimization problem over a functio

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Vultureanu-Albişi, Alexandra, Ionuţ Murareţu, and Costin Bădică. "Explainable Recommender Systems Through Reinforcement Learning and Knowledge Distillation on Knowledge Graphs." Information 16, no. 4 (2025): 282. https://doi.org/10.3390/info16040282.

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Recommender systems have evolved significantly in recent years, using advanced techniques such as explainable artificial intelligence, reinforcement learning, and graph neural networks to enhance both efficiency and transparency. This study presents a novel framework, XR2K2G (X for explainability, first R for recommender systems, the second R for reinforcement learning, first K for knowledge graph, the second K stands for knowledge distillation, and G for graph-based techniques), with the goal of developing a next-generation recommender system with a focus on careers empowerment. To optimize r

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Nie, Peng, Huanqin Wu, and Zhanchuan Cai. "Towards Automatic ICD Coding via Label Graph Generation." Mathematics 12, no. 15 (2024): 2398. http://dx.doi.org/10.3390/math12152398.

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Automatic International Classification of Disease (ICD) coding, a system for assigning proper codes to a given clinical text, has received increasing attention. Previous studies have focused on formulating the ICD coding task as a multi-label prediction approach, exploring the relationship between clinical texts and ICD codes, parent codes and child codes, and siblings. However, the large search space of ICD codes makes it difficult to localize target labels. Moreover, there exists a great unbalanced distribution of ICD codes at different levels. In this work, we propose LabGraph, which transf

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Wu, Zhihao, and Fang Jia. "Construction and Application of a Major-Specific Knowledge Graph Based on Big Data in Education." International Journal of Emerging Technologies in Learning (iJET) 17, no. 07 (2022): 64–79. http://dx.doi.org/10.3991/ijet.v17i07.30405.

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The main problems lying in the learning process of learners in different majors are that they study blindly and do not have a complex knowledge structure, which are seriously affecting their learning effects. But if a knowledge graph can be modeled for the major-specific curriculum system using the quantitative method from the perspective of knowledge network, it may be able to improve the existing teaching problems and optimize the teaching quality. The existing major-specific knowledge graphs were all constructed in an abstract form, ignoring the inherent prior learning relationship between

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Meghanathan, Natarajan. "Unit Disk Graph-Based Node Similarity Index for Complex Network Analysis." Complexity 2019 (March 14, 2019): 1–22. http://dx.doi.org/10.1155/2019/6871874.

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We seek to quantify the extent of similarity among nodes in a complex network with respect to two or more node-level metrics (like centrality metrics). In this pursuit, we propose the following unit disk graph-based approach: we first normalize the values for the node-level metrics (using the sum of the squares approach) and construct a unit disk graph of the network in a coordinate system based on the normalized values of the node-level metrics. There exists an edge between two vertices in the unit disk graph if the Euclidean distance between the two vertices in the normalized coordinate syst

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Jardine, J. F. "Stable Components and Layers." Canadian Mathematical Bulletin 63, no. 3 (2019): 562–76. http://dx.doi.org/10.4153/s000843951900064x.

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AbstractComponent graphs $\unicode[STIX]{x1D6E4}_{0}(F)$ are defined for arrays of sets $F$, and, in particular, for arrays of path components for Vietoris–Rips complexes and Lesnick complexes. The path components of $\unicode[STIX]{x1D6E4}_{0}(F)$ are the stable components of the array $F$. The stable components for the system of Lesnick complexes $\{L_{s,k}(X)\}$ for a finite data set $X$ decompose into layers, which are themselves path components of a graph. Combinatorial scoring functions are defined for layers and stable components.

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Pramanik, Tarasankar, G. Muhiuddin, Abdulaziz M. Alanazi, and Madhumangal Pal. "An Extension of Fuzzy Competition Graph and Its Uses in Manufacturing Industries." Mathematics 8, no. 6 (2020): 1008. http://dx.doi.org/10.3390/math8061008.

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Competition graph is a graph which constitutes from a directed graph (digraph) with an edge between two vertices if they have some common preys in the digraph. Moreover, Fuzzy competition graph (briefly, FCG) is the higher extension of the crisp competition graph by assigning fuzzy value to each vertex and edge. Also, Interval-valued FCG (briefly, IVFCG) is another higher extension of fuzzy competition graph by taking each fuzzy value as a sub-interval of the interval [ 0 , 1 ] . This graph arises in many real world systems; one of them is discussed as follows: Each and every species in nature

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Nirmala, A. N., and S. Kumbinarasaiah. "An intriguing numerical strategy for Zakharov–Kuznetsov equation through graph-theoretic polynomials." Physica Scripta 99, no. 9 (2024): 095267. http://dx.doi.org/10.1088/1402-4896/ad6c8e.

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Abstract This paper explores graph-theoretic polynomials to find the approximate solution of the (2+1)D Time-fractional Zakharov-Kuznetsov(TF-Z-K) equation. The Zakharov-Kuznetsov equations govern the behavior of nonlinear acoustic waves in the plasma of hot isothermal electrons and cold ions in the presence of a homogeneous magnetic field. Independence polynomials of the Ladder-Rung graph serve as the polynomial approximation for the suggested Independence Polynomial Collocation Method (IPCM). The Caputo fractional derivatives are adopted to determine the fractional derivatives in the TF-Z-K

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Pasqualetti, Fabio, Antonio Bicchi, and Francesco Bullo. "Consensus Computation in Unreliable Networks: A System Theoretic Approach." Automatic Control, IEEE Transactions on 57, no. 1 (2012): 90–104. https://doi.org/10.1109/TAC.2011.2158130.

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This work considers the problem of reaching consensus in an unreliable linear consensus network. A solution to this problem is relevant for several tasks in multi-agent systems including motion coordination, clock synchronization, and cooperative estimation. By modeling the unreliable nodes as unknown and unmeasurable inputs affecting the network, we recast the problem into an unknown-input system theoretic framework. Only relying on their direct measurements, the agents detect and identify the misbehaving agents using fault detection and isolation techniques. We consider both the case that mi

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Fujita, Takaaki. "Quasi-ultrafilters and Weak-ultrafilters: Their Properties and Maximality." Asian Research Journal of Mathematics 21, no. 3 (2025): 49–62. https://doi.org/10.9734/arjom/2025/v21i3899.

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The concept of a Quasi-Ultrafilter provides an axiomatic analysis of incomplete social judgments. The weak filter (or weak ultrafilter) was introduced by K. Schlechta in the 1990s as a relaxed version of an ultrafilter. A pair (X, f) of a finite set X and a symmetric submodular function f is called a connectivity system. This concept is commonly used in discussions of graph width parameters, such as branch-width and tree-width, to analyze graph structures. In this paper, we discussed Quasi-Ultrafilter and Maximal Quasi-filter on Connectivity System.

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Suparta, I. Nengah, Mathiyazhagan Venkatachalam, I. Gede Aris Gunadi, and Putu Andi Cipta Pratama. "GRACEFUL CHROMATIC NUMBER OF SOME CARTESIAN PRODUCT GRAPHS." Ural Mathematical Journal 9, no. 2 (2023): 193. http://dx.doi.org/10.15826/umj.2023.2.016.

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A graph \(G(V,E)\) is a system consisting of a finite non empty set of vertices \(V(G)\) and a set of edges \(E(G)\). A (proper) vertex colouring of \(G\) is a function \(f:V(G)\rightarrow \{1,2,\ldots,k\},\) for some positive integer \(k\) such that \(f(u)\neq f(v)\) for every edge \(uv\in E(G)\). Moreover, if \(|f(u)-f(v)|\neq |f(v)-f(w)|\) for every adjacent edges \(uv,vw\in E(G)\), then the function \(f\) is called graceful colouring for \(G\). The minimum number \(k\) such that \(f\) is a graceful colouring for \(G\) is called the graceful chromatic number of \(G\). The purpose of this re

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BUDKO, NIKITA P. "THE METHOD OF SYNTHESIS OF THE SUBSYSTEM OF INTELLIGENT MONITORING OF THE INFORMATION AND TELECOMMUNICATIONS NETWORK OF THE SITUATION CENTER." H&ES Research 13, no. 5 (2021): 38–56. http://dx.doi.org/10.36724/2409-5419-2021-13-5-38-56.

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Introduction: in accordance with the task of forming a system of distributed situational centers of public authorities, it is necessary to interface heterogeneous segments of the department's information and telecommunications networks into a geographically distributed infrastructure with the construction of a subsystem for monitoring the state of its elements on it. The purpose of the study: based on the use of basic concepts of structural synthesis methods, structural analysis of network infrastructures, as well as parametric synthesis procedures, to develop a methodology for the synthesis o

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Nhi, Nguyen Thi Uyen, Thanh Manh Le, and Thanh The Van. "A Model of Semantic-Based Image Retrieval Using C-Tree and Neighbor Graph." International Journal on Semantic Web and Information Systems 18, no. 1 (2022): 1–23. http://dx.doi.org/10.4018/ijswis.295551.

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The problems of image mining and semantic image retrieval play an important role in many areas of life. In this paper, a semantic-based image retrieval system is proposed that relies on the combination of C-Tree, which was built in our previous work, and a neighbor graph (called Graph-CTree) to improve accuracy. The k-Nearest Neighbor (k-NN) algorithm is used to classify a set of similar images that are retrieved on Graph-CTree to create a set of visual words. An ontology framework for images is created semi-automatically. SPARQL query is automatically generated from visual words and retrieve

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Oz, Mert Sinan, Roberto Cruz, and Juan Rada. "Computation method of the Hosoya index of primitive coronoid systems." Mathematical Biosciences and Engineering 19, no. 10 (2022): 9842–52. http://dx.doi.org/10.3934/mbe.2022458.

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<abstract><p>Coronoid systems are natural graph representations of coronoid hydrocarbons associated with benzenoid systems, but they differ in that they contain a hole. The Hosoya index of a graph $ G $ is defined as the total number of independent edge sets, that are called $ k $-matchings in $ G $.</p> <p>The Hosoya index is a significant molecular descriptor that has an important position in QSAR and QSPR studies. Therefore, the computation of the Hosoya index of various molecular graphs is needed for making progress on investigations. In this paper, a method based o

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NI, TIAN-JIA, and ZHI-YING WEN. "SELF-SIMILARITY OF SATISFIABLE BOOLEAN EXPRESSIONS DECIPHERED IN TERMS OF GRAPH DIRECTED ITERATED FUNCTION SYSTEMS." Fractals 16, no. 04 (2008): 305–15. http://dx.doi.org/10.1142/s0218348x0800406x.

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The decision problem of satisfiability of Boolean expression in k-conjunctive normal form (kSAT) is a typical NP-complete problem. In this paper, by mapping the whole Boolean expressions in k-conjunctive normal form onto a unit hypercube, we visualize the problem space of kSAT. The pattern of kSAT is shown to have self-similarity which can be deciphered in terms of graph directed iterated function system. We provide that the Hausdorff dimension of the pattern of kSAT is equal to the box-counting dimension and increases with k. This suggests that the time complexity of kSAT increases with k.

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Salihoglu, Semih. "Kùzu: A Database Management System For "Beyond Relational" Workloads." ACM SIGMOD Record 52, no. 3 (2023): 39–40. http://dx.doi.org/10.1145/3631504.3631514.

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I would like to share my opinions on the following question: how should a modern graph DBMS (GDBMS) be architected? This is the motivating research question we are addressing in the K`uzu project at University of Waterloo [4, 5].1 I will argue that a modern GDBMS should optimize for a set of what I will call, for lack of a better term, "beyond relational" workloads. As a background, let me start with a brief overview of GDBMSs.

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Usha, Subramaniam, Murugesan Karthik, Marappan Jothibasu, and Vijayaragavan Gowtham. "An integrated exploration of heat kernel invariant feature and manifolding technique for 3D object recognition system." Acta Scientiarum. Technology 46, no. 1 (2023): e62608. http://dx.doi.org/10.4025/actascitechnol.v46i1.62608.

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Spectral Graph theory has been utilized frequently in the field of Computer Vision and Pattern Recognition to address challenges in the field of Image Segmentation and Image Classification. In the proposed method, for classification techniques, the associated graph's Eigen values and Eigen vectors of the adjacency matrix or Laplacian matrix created from the images are employed. The Laplacian spectrum and a graph's heat kernel are inextricably linked. Exponentiating the Laplacian eigensystem over time yields the heat kernel, which is the solution to the heat equations. In the proposed technique

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Jiang, Yaozhi. "Dialectical Logic K-Model: the Discrete Time Dynamical Sampling System, Multidimensional Logic Variable and Associate Database(ADB)." Journal of Mathematics Research 10, no. 2 (2018): 88. http://dx.doi.org/10.5539/jmr.v10n2p88.

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Following the earlier works about dialectical logic K-model by the author, in this succeed paper author described the three problems : the first is that discrete time dynamical sampling system to solve which the true-value function is unknown and need discrete time dynamical sampling system to obtain a series of sampled discrete time true-value function points to predict the continuous true-value function or we need some properties of true value function in the frequency domain, a several formulas for true-value function of single-dimensional logic variable via discrete Fourier transformation

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Liu, Jiafei, Shuming Zhou, Zhendong Gu, Yihong Wang, and Qianru Zhou. "A Note of Independent Number and Domination Number of Qn,k,m-Graph." Parallel Processing Letters 29, no. 03 (2019): 1950011. http://dx.doi.org/10.1142/s0129626419500117.

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The independent number and domination number are two essential parameters to assess the resilience of the interconnection network of multiprocessor systems which is usually modeled by a graph. The independent number, denoted by [Formula: see text], of a graph [Formula: see text] is the maximum cardinality of any subset [Formula: see text] such that no two elements in [Formula: see text] are adjacent in [Formula: see text]. The domination number, denoted by [Formula: see text], of a graph [Formula: see text] is the minimum cardinality of any subset [Formula: see text] such that every vertex in

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