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1

Hilton, N. Zoe, Elke Ham, Kevin L. Nunes, Nicole C. Rodrigues, Cairina Frank, and Michael C. Seto. "Using Graphs to Improve Violence Risk Communication." Criminal Justice and Behavior 44, no. 5 (2016): 678–94. http://dx.doi.org/10.1177/0093854816668916.

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We examined the use of graphs as an aid to communicating statistical risk among forensic clinicians. We first tested four graphs previously used or recommended for forensic risk assessment among 442 undergraduate students who made security recommendations about two offenders whose risk differed by one actuarial category of risk for violent recidivism (Study 1). Effective decision making was defined as actuarially higher risk offenders being assigned to greater security than lower risk offenders. The graph resulting in the largest distinction among less numerate students was a probability bar g
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2

SHOUBRIDGE, PETER, MIRO KRAETZL, WAL WALLIS, and HORST BUNKE. "DETECTION OF ABNORMAL CHANGE IN A TIME SERIES OF GRAPHS." Journal of Interconnection Networks 03, no. 01n02 (2002): 85–101. http://dx.doi.org/10.1142/s0219265902000562.

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In the management of large enterprise communication networks, it becomes difficult to detect and identify causes of abnormal change in traffic distributions when the underlying logical topology is dynamic. This paper describes a novel approach to abnormal network change detection by representing periodic observations of logical communications within a network as a time series of graphs. A number of graph distance measures are proposed to assess the difference between successive graphs and identify abnormal behaviour. Localisation techniques have also been described to show where in the network
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3

Kusper, Gábor, and Csaba Biró. "Convert a Strongly Connected Directed Graph to a Black-and-White 3-SAT Problem by the Balatonboglár Model." Algorithms 13, no. 12 (2020): 321. http://dx.doi.org/10.3390/a13120321.

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In a previous paper we defined the black and white SAT problem which has exactly two solutions, where each variable is either true or false. We showed that black and white 2-SAT problems represent strongly connected directed graphs. We presented also the strong model of communication graphs. In this work we introduce two new models, the weak model, and the Balatonboglár model of communication graphs. A communication graph is a directed graph, where no self loops are allowed. In this work we show that the weak model of a strongly connected communication graph is a black and white SAT problem. W
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4

LI, YINKUI, ZONGTIAN WEI, XIAOKUI YUE, and ERQIANG LIU. "TENACITY OF TOTAL GRAPHS." International Journal of Foundations of Computer Science 25, no. 05 (2014): 553–62. http://dx.doi.org/10.1142/s012905411450021x.

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Communication networks must be constructed to be as stable as possible, not only with the respect to the initial disruption, but also with respect to the possible reconstruction. Many graph theoretical parameters have been used to describe the stability of communication networks. Tenacity is a reasonable one, which shows not only the difficulty to break down the network but also the damage that has been caused. Total graphs are the largest graphs formed by the adjacent relations of elements of a graph. Thus, total graphs are highly recommended for the design of interconnection networks. In thi
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Alanazi, A. M., G. Muhiuddin, A. R. Kannan, and V. Govindan. "New Perspectives on Classical Meanness of Some Ladder Graphs." Journal of Mathematics 2021 (June 30, 2021): 1–14. http://dx.doi.org/10.1155/2021/9926350.

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In this study, we investigate a new kind of mean labeling of graph. The ladder graph plays an important role in the area of communication networks, coding theory, and transportation engineering. Also, we found interesting new results corresponding to classical mean labeling for some ladder-related graphs and corona of ladder graphs with suitable examples.
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Eshaghian, Mary Mehrnoosh. "MAPPING ARBITRARY HETEROGENEOUS TASK GRAPHS ONTO ARBITRARY HETEROGENEOUS SYSTEM GRAPH." International Journal of Foundations of Computer Science 12, no. 05 (2001): 599–628. http://dx.doi.org/10.1142/s0129054101000680.

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In this paper, a generic technique for mapping arbitrary heterogeneous task graphs onto arbitrary heterogeneous system graphs is presented. The heterogeneous task and system graphs studied in this paper have nonuniform computation and communication weights associated with the nodes and the edges. Two clustering algorithms have been proposed that can be used to obtain a multilayer clustered graph called a Spec graph from a given task graph and a multilayer clustered graph called a Rep graph from a given system graph. We present a mapping algorithm that produces a suboptimal matching of a given
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Manjusha, O. T. "Set Domination in Fuzzy Graphs Using Strong Arcs." Pan-American Journal of Mathematics 1 (August 3, 2022): 9. http://dx.doi.org/10.28919/cpr-pajm/1-9.

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Set domination in fuzzy graphs is very useful for solving traffic problems during communication in computer networks and travelling networks. In this article, the concept of set domination in fuzzy graphs using strong arcs is introduced. The strong set domination number of complete fuzzy graph and complete bipartite fuzzy graph is determined. It is obtained the properties of the new parameter and related it to some other known domination parameters of fuzzy graphs. An upper bound for the strong set domination number of fuzzy graphs is also obtained.
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Yang, Chao, Bing Yao, Hong Yu Wang, Xiang'en Chen, and Si Hua Yang. "Graph Colorings Applied in Scale-Free Networks." Advanced Materials Research 760-762 (September 2013): 2199–204. http://dx.doi.org/10.4028/www.scientific.net/amr.760-762.2199.

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Building up graph models to simulate scale-free networks is an important method since graphs have been used in researching scale-free networks and communication networks, such as graph colorings can be used for distinguishing objects of communication and information networks. In this paper we determine the avdtc chromatic numbers of some models related with researching networks.
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9

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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10

Manghi, Paolo, Claudio Atzori, Michele De Bonis, and Alessia Bardi. "Entity deduplication in big data graphs for scholarly communication." Data Technologies and Applications 54, no. 4 (2020): 409–35. http://dx.doi.org/10.1108/dta-09-2019-0163.

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PurposeSeveral online services offer functionalities to access information from “big research graphs” (e.g. Google Scholar, OpenAIRE, Microsoft Academic Graph), which correlate scholarly/scientific communication entities such as publications, authors, datasets, organizations, projects, funders, etc. Depending on the target users, access can vary from search and browse content to the consumption of statistics for monitoring and provision of feedback. Such graphs are populated over time as aggregations of multiple sources and therefore suffer from major entity-duplication problems. Although dedu
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11

Wang, Hong Yu, Bing Yao, Chao Yang, et al. "Edge-Magic Total Labellings of some Network Models." Applied Mechanics and Materials 347-350 (August 2013): 2752–57. http://dx.doi.org/10.4028/www.scientific.net/amm.347-350.2752.

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It has been known that edge-symmetric graphs can be used as models of some scale-free networks, such as hierarchial networks and self-similar networks, such as graph colorings can be used for distinguishing objects of communication and informa-tion networks. We study the edge-magic property of edge-symmetric graphs, and construct graphs having edge-magic total labellings from smaller graphs.
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12

Turaci, Tufan, and Hüseyin Aksan. "The Vulnerability of Some Networks including Cycles via Domination Parameters." Journal of Optimization 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/4705493.

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LetG=(V(G),E(G))be an undirected simple connected graph. A network is usually represented by an undirected simple graph where vertices represent processors and edges represent links between processors. Finding the vulnerability values of communication networks modeled by graphs is important for network designers. The vulnerability value of a communication network shows the resistance of the network after the disruption of some centers or connection lines until a communication breakdown. The domination number and its variations are the most important vulnerability parameters for network vulnera
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13

MATHEW, SUNIL. "ON CYCLE CONNECTIVITY OF GRAPHS." Journal of Interconnection Networks 13, no. 01n02 (2012): 1250005. http://dx.doi.org/10.1142/s0219265912500053.

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In this article, the concept of cycle connectivity of a weighted graph is discussed. Cycle connectivity of partial trees, cycles and precisely weighted graphs are obtained. Also the concepts of cyclic cutnode and cyclic bridge in weighted graphs are introduced and a condition for a precisely weighted graph to possess a cyclic cutnode is obtained.
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14

Yang, Hong, Muhammad Siddiqui, Muhammad Ibrahim, Sarfraz Ahmad, and Ali Ahmad. "Computing The Irregularity Strength of Planar Graphs." Mathematics 6, no. 9 (2018): 150. http://dx.doi.org/10.3390/math6090150.

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The field of graph theory plays a vital role in various fields. One of the important areas in graph theory is graph labeling used in many applications such as coding theory, X-ray crystallography, radar, astronomy, circuit design, communication network addressing, and data base management. In this paper, we discuss the totally irregular total k labeling of three planar graphs. If such labeling exists for minimum value of a positive integer k, then this labeling is called totally irregular total k labeling and k is known as the total irregularity strength of a graph G. More preciously, we deter
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15

Weaver, Nik. "Quantum Graphs as Quantum Relations." Journal of Geometric Analysis 31, no. 9 (2021): 9090–112. http://dx.doi.org/10.1007/s12220-020-00578-w.

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AbstractThe “noncommutative graphs” which arise in quantum error correction are a special case of the quantum relations introduced in Weaver (Quantum relations. Mem Am Math Soc 215(v–vi):81–140, 2012). We use this perspective to interpret the Knill–Laflamme error-correction conditions (Knill and Laflamme in Theory of quantum error-correcting codes. Phys Rev A 55:900-911, 1997) in terms of graph-theoretic independence, to give intrinsic characterizations of Stahlke’s noncommutative graph homomorphisms (Stahlke in Quantum zero-error source-channel coding and non-commutative graph theory. IEEE Tr
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16

SHERMAN, DAVID, MING TSAI, CHENG-KUAN LIN, et al. "4-ORDERED HAMILTONICITY FOR SOME CHORDAL RING GRAPHS." Journal of Interconnection Networks 11, no. 03n04 (2010): 157–74. http://dx.doi.org/10.1142/s0219265910002787.

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A graph G is k-ordered if for any sequence of k distinct vertices of G, there exists a cycle in G containing these k vertices in the specified order. It is k-ordered Hamiltonian if, in addition, the required cycle is Hamiltonian. The question of the existence of an infinite class of 3-regular 4-ordered Hamiltonian graphs was posed in 1997 by Ng and Schultz.13At the time, the only known examples were K4and K3,3. Some progress was made in 2008 by Mészáros,12when the Peterson graph was found to be 4-ordered and the Heawood graph was proved to be 4-ordered Hamiltonian; moreover, an infinite class
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17

Kamath, S. S., A. Senthil Thilak, and M. Rashmi. "Algorithmic aspects of k-part degree restricted domination in graphs." Discrete Mathematics, Algorithms and Applications 12, no. 05 (2020): 2050057. http://dx.doi.org/10.1142/s1793830920500573.

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The concept of network is predominantly used in several applications of computer communication networks. It is also a fact that the dominating set acts as a virtual backbone in a communication network. These networks are vulnerable to breakdown due to various causes, including traffic congestion. In such an environment, it is necessary to regulate the traffic so that these vulnerabilities could be reasonably controlled. Motivated by this, [Formula: see text]-part degree restricted domination is defined as follows. For a positive integer [Formula: see text], a dominating set [Formula: see text]
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18

Zhu, Chun Jiang, Tan Zhu, Kam-Yiu Lam, Song Han, and Jinbo Bi. "Communication-Optimal Distributed Dynamic Graph Clustering." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 5957–64. http://dx.doi.org/10.1609/aaai.v33i01.33015957.

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We consider the problem of clustering graph nodes over large-scale dynamic graphs, such as citation networks, images and web networks, when graph updates such as node/edge insertions/deletions are observed distributively. We propose communication-efficient algorithms for two well-established communication models namely the message passing and the blackboard models. Given a graph with n nodes that is observed at s remote sites over time [1,t], the two proposed algorithms have communication costs Õ(ns) and Õ(n + s) (Õ hides a polylogarithmic factor), almost matching their lower bounds, Ω(ns) and
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19

Finta, Lucian, and Zhen Liu. "Complexity of Task Graph Scheduling with Fixed Communication Capacity." International Journal of Foundations of Computer Science 08, no. 01 (1997): 43–66. http://dx.doi.org/10.1142/s0129054197000045.

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Consider a scheduling problem of parallel computations in multiprocessor systems. Let a parallel program be modeled by a task graph, where vertices represent tasks and arcs the communications between tasks. An interprocessor communication time incurs when two tasks assigned to two different processors have to communicate. Such a scheduling problem has recently been studied in the literature, mostly for the case where interprocessor communication times are fully determined. In this paper, we consider the scheduling problem with communication resource constraints. More specifically, we consider
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20

Elahi, Kashif, Ali Ahmad, and Roslan Hasni. "Construction Algorithm for Zero Divisor Graphs of Finite Commutative Rings and Their Vertex-Based Eccentric Topological Indices." Mathematics 6, no. 12 (2018): 301. http://dx.doi.org/10.3390/math6120301.

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Chemical graph theory is a branch of mathematical chemistry which deals with the non-trivial applications of graph theory to solve molecular problems. Graphs containing finite commutative rings also have wide applications in robotics, information and communication theory, elliptic curve cryptography, physics, and statistics. In this paper we discuss eccentric topological indices of zero divisor graphs of commutative rings Z p 1 p 2 × Z q , where p 1 , p 2 , and q are primes. To enhance the importance of these indices a construction algorithm is also devised for zero divisor graphs of commutati
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Zhang, Xianhang, Hanchen Wang, Jianke Yu, Chen Chen, Xiaoyang Wang, and Wenjie Zhang. "Polarity-based graph neural network for sign prediction in signed bipartite graphs." World Wide Web 25, no. 2 (2022): 471–87. http://dx.doi.org/10.1007/s11280-022-01015-4.

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AbstractAs a fundamental data structure, graphs are ubiquitous in various applications. Among all types of graphs, signed bipartite graphs contain complex structures with positive and negative links as well as bipartite settings, on which conventional graph analysis algorithms are no longer applicable. Previous works mainly focus on unipartite signed graphs or unsigned bipartite graphs separately. Several models are proposed for applications on the signed bipartite graphs by utilizing the heuristic structural information. However, these methods have limited capability to fully capture the info
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22

Erlebach, Thomas, and Jakob T. Spooner. "Exploration of k-edge-deficient temporal graphs." Acta Informatica 59, no. 4 (2022): 387–407. http://dx.doi.org/10.1007/s00236-022-00421-5.

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AbstractA temporal graph with lifetime L is a sequence of L graphs $$G_1, \ldots ,G_L$$ G 1 , … , G L , called layers, all of which have the same vertex set V but can have different edge sets. The underlying graph is the graph with vertex set V that contains all the edges that appear in at least one layer. The temporal graph is always connected if each layer is a connected graph, and it is k-edge-deficient if each layer contains all except at most k edges of the underlying graph. For a given start vertex s, a temporal exploration is a temporal walk that starts at s, traverses at most one edge
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TAMASSIA, ROBERTO, IOANNIS G. TOLLIS, and JEFFREY SCOTT VITTER. "A Parallel Algorithm for Planar Orthogonal Grid Drawings." Parallel Processing Letters 10, no. 01 (2000): 141–50. http://dx.doi.org/10.1142/s0129626400000147.

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In this paper we consider the problem of constructing planar orthogonal grid drawings (or more simply, layouts) of graphs, with the goal of minimizing the number of bends along the edges. We present optimal parallel algorithms that construct graph layouts with O(n) maximum edge length, O(n2) area, and at most 2n+4 bends (for biconnected graphs) and 2.4n+2 bends (for simply connected graphs). All three of these quality measures for the layouts are optimal in the worst case for biconnected graphs. The algorithm runs on a CREW PRAM in O( log n) time with n/ log n processors, thus achieving optima
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Hayat, Khizar, Muhammad Irfan Ali, Bing-Yuan Cao, and Xiao-Peng Yang. "A New Type-2 Soft Set: Type-2 Soft Graphs and Their Applications." Advances in Fuzzy Systems 2017 (2017): 1–17. http://dx.doi.org/10.1155/2017/6162753.

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The correspondence between a vertex and its neighbors has an essential role in the structure of a graph. Type-2 soft sets are also based on the correspondence of primary parameters and underlying parameters. In this study, we present an application of type-2 soft sets in graph theory. We introduce vertex-neighbors based type-2 soft sets overX(set of all vertices of a graph) andE(set of all edges of a graph). Moreover, we introduce some type-2 soft operations in graphs by presenting several examples to demonstrate these new concepts. Finally, we describe an application of type-2 soft graphs in
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Anderson, Jacob, and Geoffrey A. Hollinger. "Communication Planning for Cooperative Terrain-Based Underwater Localization." Sensors 21, no. 5 (2021): 1675. http://dx.doi.org/10.3390/s21051675.

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This paper presents a decentralized communication planning algorithm for cooperative terrain-based navigation (dec-TBN) with autonomous underwater vehicles. The proposed algorithm uses forward simulation to approximate the value of communicating at each time step. The simulations are used to build a directed acyclic graph that can be searched to provide a minimum cost communication schedule. Simulations and field trials are used to validate the algorithm. The simulations use a real-world bathymetry map from Lake Nighthorse, CO, and a sensor model derived from an Ocean Server Iver2 vehicle. The
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Preston, Ronald V., and Amanda S. Garner. "Representation as a Vehicle for Solving and Communication." Mathematics Teaching in the Middle School 9, no. 1 (2003): 38–43. http://dx.doi.org/10.5951/mtms.9.1.0038.

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Students in MS. Simpson's seventh-grade prealgebra class were challenged to use data to decide which of several class party plans was best. Because Takisha focused on price, she preferred using a table to justify her decision. Samantha used a written explanation to determine for herself which plan was best. Brandon's group used a table that indicated the price per person. However, when it came to convincing others of the best plan, some students chose other representations. For example, Brandon decided to use his graphing calculator to display linear graphs of the three plans. Melissa decided
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Zhou, Xiaoqing, Mustafa Habib, Tariq Javeed Zia, Asim Naseem, Anila Hanif, and Ansheng Ye. "Topological invariants for the line graphs of some classes of graphs." Open Chemistry 17, no. 1 (2019): 1483–90. http://dx.doi.org/10.1515/chem-2019-0154.

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AbstractGraph theory plays important roles in the fields of electronic and electrical engineering. For example, it is critical in signal processing, networking, communication theory, and many other important topics. A topological index (TI) is a real number attached to graph networks and correlates the chemical networks with physical and chemical properties, as well as with chemical reactivity. In this paper, our aim is to compute degree-dependent TIs for the line graph of the Wheel and Ladder graphs. To perform these computations, we first computed M-polynomials and then from the M-polynomial
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Draief, M., A. Ganesh, and L. Massoulié. "Exponential Random Graphs as Models of Overlay Networks." Journal of Applied Probability 46, no. 1 (2009): 199–220. http://dx.doi.org/10.1239/jap/1238592125.

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In this paper we give an analytic solution for graphs withnnodes andE=cnlognedges for which the probability of obtaining a given graphGisµn(G) = exp (-β∑i=1ndi2), wherediis the degree of nodei. We describe how this model appears in the context of load balancing in communication networks, namely peer-to-peer overlays. We then analyse the degree distribution of such graphs and show that the degrees are concentrated around their mean value. Finally, we derive asymptotic results for the number of edges crossing a graph cut and use these results (i) to compute the graph expansion and conductance, a
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Saha, Arindam, James A. R. Marshall, and Andreagiovanni Reina. "Memory and communication efficient algorithm for decentralized counting of nodes in networks." PLOS ONE 16, no. 11 (2021): e0259736. http://dx.doi.org/10.1371/journal.pone.0259736.

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Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor networks. Thus several stochastic and naïve deterministic algorithms for distributed graph size estimation or calculation have been provided. Here we present a deterministic and distributed algorithm that allows every node of a connected graph to determine the graph size in finite time, if an upper bound on the graph size is provided. The algorithm consists in
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GU, WEIZHEN, and KIRSTI WASH. "BOUNDS ON THE DOMINATION NUMBER OF PERMUTATION GRAPHS." Journal of Interconnection Networks 10, no. 03 (2009): 205–17. http://dx.doi.org/10.1142/s0219265909002522.

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For a graph G with n vertices and a permutation α on V(G), a permutation graph Pα(G) is obtained from two identical copies of G by adding an edge between v and α(V) for any v ϵ V(G). Let γ(G) be the domination number of a graph G. It has been shown that γ(G) ≤ γ(Pα(G) ≤ 2γ(G) for any permutation α on V(G). In this paper, we investigate specific graphs for which there exists a permutation α such that γ(Pα(G)) ≻ γ(G) in terms of the domination number of G or the maximum degree of G. Additionally, we construct a class of graphs for which the domination number of any permutation graph is twice the
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BHABAK, PUSPAL, and HOVHANNES A. HARUTYUNYAN. "Approximation Algorithm for the Broadcast Time in k-Path Graph." Journal of Interconnection Networks 19, no. 04 (2019): 1950006. http://dx.doi.org/10.1142/s0219265919500063.

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Broadcasting is an information dissemination problem in a connected network in which one node, called the originator, must distribute a message to all other nodes by placing a series of calls along the communication lines of the network. In every unit of time, the informed nodes aid the originator in distributing the message. Finding the broadcast time of any vertex in an arbitrary graph is NP-complete. The polynomial time solvability is shown only for certain graphs like trees, unicyclic graphs, tree of cycles, necklace graphs, fully connected trees and tree of cliques. In this paper we study
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Draief, M., A. Ganesh, and L. Massoulié. "Exponential Random Graphs as Models of Overlay Networks." Journal of Applied Probability 46, no. 01 (2009): 199–220. http://dx.doi.org/10.1017/s0021900200005313.

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In this paper we give an analytic solution for graphs with n nodes and E = cn log n edges for which the probability of obtaining a given graph G is µn (G) = exp (- β ∑i=1 n d i 2), where d i is the degree of node i. We describe how this model appears in the context of load balancing in communication networks, namely peer-to-peer overlays. We then analyse the degree distribution of such graphs and show that the degrees are concentrated around their mean value. Finally, we derive asymptotic results for the number of edges crossing a graph cut and use these results (i) to compute the graph expans
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Zeng, Yong, Yixin Li, Zhongyuan Jiang, and Jianfeng Ma. "GNS: Forge High Anonymity Graph by Nonlinear Scaling Spectrum." Security and Communication Networks 2021 (September 30, 2021): 1–11. http://dx.doi.org/10.1155/2021/8609278.

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It is crucial to generate random graphs with specific structural properties from real graphs, which could anonymize graphs or generate targeted graph data sets. The state-of-the-art method called spectral graph forge (SGF) was proposed at INFOCOM 2018. This method uses a low-rank approximation of the matrix by throwing away some spectrums, which provides privacy protection after distributing graphs while ensuring data availability to a certain extent. As shown in SGF, it needs to discard at least 20% spectrum to defend against deanonymous attacks. However, the data availability will be signifi
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Jarrar, Mustafa, and Anton Deik. "The Graph Signature." International Journal on Semantic Web and Information Systems 11, no. 2 (2015): 36–65. http://dx.doi.org/10.4018/ijswis.2015040102.

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Querying large data graphs has brought the attention of the research community. Many solutions were proposed, such as Oracle Semantic Technologies, Virtuoso, RDF3X, and C-Store, among others. Although such approaches have shown good performance in queries with medium complexity, they perform poorly when the complexity of the queries increases. In this paper, the authors propose the Graph Signature Index, a novel and scalable approach to index and query large data graphs. The idea is that they summarize a graph and instead of executing the query on the original graph, they execute it on the sum
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LIN, LAN, and YIXUN LIN. "The Minimum Stretch Spanning Tree Problem for Hamming Graphs and Higher-Dimensional Grids." Journal of Interconnection Networks 20, no. 01 (2020): 2050004. http://dx.doi.org/10.1142/s0219265920500048.

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The minimum stretch spanning tree problem for a graph G is to find a spanning tree T of G such that the maximum distance in T between two adjacent vertices is minimized. The minimum value of this optimization problem gives rise to a graph invariant σ(G), called the tree-stretch of G. The problem has been proved NP-hard. In this paper we present a general approach to determine the exact values σ(G) for a series of typical graphs arising from communication networks, such as Hamming graphs and higher-dimensional grids (including hypercubes).
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ZHANG, YINGYING, and XIAOYU ZHU. "Proper Vertex Connection and Graph Operations." Journal of Interconnection Networks 19, no. 02 (2019): 1950001. http://dx.doi.org/10.1142/s0219265919500014.

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A path in a vertex-colored graph is a vertex-proper path if any two internal adjacent vertices differ in color. A vertex-colored graph is proper vertex k-connected if any two vertices of the graph are connected by k disjoint vertex-proper paths of the graph. For a k-connected graph G, the proper vertex k-connection number of G, denoted by pvck(G), is defined as the smallest number of colors required to make G proper vertex k-connected. A vertex-colored graph is strong proper vertex-connected, if for any two vertices u, v of the graph, there exists a vertex-proper u-v geodesic. For a connected
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Atkins, Rachel M., and Karen S. McNeal. "Exploring Differences Among Student Populations During Climate Graph Reading Tasks: An Eye Tracking Study." Journal of Astronomy & Earth Sciences Education (JAESE) 5, no. 2 (2018): 85–114. http://dx.doi.org/10.19030/jaese.v5i2.10219.

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Communicating climate information is challenging due to the interdisciplinary nature of the topic along with compounding cognitive and affective learning challenges. Graphs are a common representation used by scientists to communicate evidence of climate change. However, it is important to identify how and why individuals on the continuum of expertise navigate graphical data differently as this has implications for effective communication of this information. We collected and analyzed eye-tracking metrics of geoscience graduate students and novice undergraduate students while viewing graphs di
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Min, Seung Won, Kun Wu, Sitao Huang, et al. "Large graph convolutional network training with GPU-oriented data communication architecture." Proceedings of the VLDB Endowment 14, no. 11 (2021): 2087–100. http://dx.doi.org/10.14778/3476249.3476264.

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Graph Convolutional Networks (GCNs) are increasingly adopted in large-scale graph-based recommender systems. Training GCN requires the minibatch generator traversing graphs and sampling the sparsely located neighboring nodes to obtain their features. Since real-world graphs often exceed the capacity of GPU memory, current GCN training systems keep the feature table in host memory and rely on the CPU to collect sparse features before sending them to the GPUs. This approach, however, puts tremendous pressure on host memory bandwidth and the CPU. This is because the CPU needs to (1) read sparse f
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Li, Zitong, Xiang Cheng, Lixiao Sun, Ji Zhang, and Bing Chen. "A Hierarchical Approach for Advanced Persistent Threat Detection with Attention-Based Graph Neural Networks." Security and Communication Networks 2021 (May 4, 2021): 1–14. http://dx.doi.org/10.1155/2021/9961342.

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Advanced Persistent Threats (APTs) are the most sophisticated attacks for modern information systems. Currently, more and more researchers begin to focus on graph-based anomaly detection methods that leverage graph data to model normal behaviors and detect outliers for defending against APTs. However, previous studies of provenance graphs mainly concentrate on system calls, leading to difficulties in modeling network behaviors. Coarse-grained correlation graphs depend on handcrafted graph construction rules and, thus, cannot adequately explore log node attributes. Besides, the traditional Grap
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Zeen El Deen, Mohamed R., and Ghada Elmahdy. "New classes of graphs with edge $ \; \delta- $ graceful labeling." AIMS Mathematics 7, no. 3 (2022): 3554–89. http://dx.doi.org/10.3934/math.2022197.

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<abstract><p>Graph labeling is a source of valuable mathematical models for an extensive range of applications in technologies (communication networks, cryptography, astronomy, data security, various coding theory problems). An edge $ \; \delta - $ graceful labeling of a graph $ G $ with $ p\; $ vertices and $ q\; $ edges, for any positive integer $ \; \delta $, is a bijective $ \; f\; $ from the set of edge $ \; E(G)\; $ to the set of positive integers $ \; \{ \delta, \; 2 \delta, \; 3 \delta, \; \cdots\; , \; q\delta\; \} $ such that all the vertex labels $ \; f^{\ast} [V(G)] $,
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RAFE, VAHID, and ADEL T. RAHMANI. "A NOVEL APPROACH TO VERIFY GRAPH SCHEMA-BASED SOFTWARE SYSTEMS." International Journal of Software Engineering and Knowledge Engineering 19, no. 06 (2009): 857–70. http://dx.doi.org/10.1142/s0218194009004398.

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Graph Grammars have recently become more and more popular as a general formal modeling language. Behavioral modeling of dynamic systems and model to model transformations are a few well-known examples in which graphs have proven their usefulness in software engineering. A special type of graph transformation systems is layered graphs. Layered graphs are a suitable formalism for modeling hierarchical systems. However, most of the research so far concentrated on graph transformation systems as a modeling means, without considering the need for suitable analysis tools. In this paper we concentrat
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Ni, Xiang, Jing Li, Mo Yu, Wang Zhou, and Kun-Lung Wu. "Generalizable Resource Allocation in Stream Processing via Deep Reinforcement Learning." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 01 (2020): 857–64. http://dx.doi.org/10.1609/aaai.v34i01.5431.

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This paper considers the problem of resource allocation in stream processing, where continuous data flows must be processed in real time in a large distributed system. To maximize system throughput, the resource allocation strategy that partitions the computation tasks of a stream processing graph onto computing devices must simultaneously balance workload distribution and minimize communication. Since this problem of graph partitioning is known to be NP-complete yet crucial to practical streaming systems, many heuristic-based algorithms have been developed to find reasonably good solutions. I
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LÜ, HUAZHONG, and TINGZENG WU. "Fractional Matching Preclusion for Restricted Hypercube-Like Graphs." Journal of Interconnection Networks 19, no. 03 (2019): 1940010. http://dx.doi.org/10.1142/s0219265919400103.

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The restricted hypercube-like graphs, variants of the hypercube, were proposed as desired interconnection networks of parallel systems. The matching preclusion number of a graph is the minimum number of edges whose deletion results in the graph with neither perfect matchings nor almost perfect matchings. The fractional perfect matching preclusion and fractional strong perfect matching preclusion are generalizations of the matching preclusion. In this paper, we obtain fractional matching preclusion number and fractional strong matching preclusion number of restricted hypercube-like graphs, whic
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Mufti, Zeeshan Saleem, Eiman Fatima, Rukhshanda Anjum, Fairouz Tchier, Qin Xin, and Md Moyazzem Hossain. "Computing First and Second Fuzzy Zagreb Indices of Linear and Multiacyclic Hydrocarbons." Journal of Function Spaces 2022 (March 22, 2022): 1–8. http://dx.doi.org/10.1155/2022/6281592.

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Fuzzy graph theory was invented by Rosenfeld. It is the extension of the work of L.A. Zadeh on fuzzy sets. Rosenfeld extracted the fuzzy-related concepts using the graph theoretic concepts. Topological indices for crisp theory have already been discussed in the literature but these days, topological index-related fuzzy graphs are much popular. Fuzzy graphs are being used as an application in different fields of sciences such as broadcast, communications, producing, social network, man-made reasoning, data hypothesis, and neural systems. In this paper, we have computed some fuzzy topological in
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Marbel, Revital, Boaz Ben-Moshe, and Tal Grinshpoun. "Urban Free-Space Optical Network Optimization." Applied Sciences 10, no. 21 (2020): 7872. http://dx.doi.org/10.3390/app10217872.

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This paper presents a set of graph optimization problems related to free-space optical communication networks. Such laser-based wireless networks require a line of sight to enable communication, thus a visibility graph model is used herein. The main objective is to provide connectivity from a communication source point to terminal points through the use of some subset of available intermediate points. To this end, we define a handful of problems that differ mainly in the costs applied to the nodes and/or edges of the graph. These problems should be optimized with respect to cost and performanc
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OBRENIĆ, BOJANA. "APPROXIMATING HYPERCUBES BY INDEX-SHUFFLE GRAPHS VIA DIRECT-PRODUCT EMULATIONS." Journal of Interconnection Networks 05, no. 04 (2004): 429–73. http://dx.doi.org/10.1142/s0219265904001258.

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Index-shuffle graphs are a family of bounded-degree hypercube-like interconnection networks for parallel computers, introduced by [Baumslag and Obrenić (1997): Index-Shuffle Graphs, …], as an efficient substitute for two standard families of hypercube derivatives: butterflies and shuffle-exchange graphs. In the theoretical framework of graph embedding and network emulations, this paper shows that the index-shuffle graph efficiently approximates the direct-product structure of the hypercube, and thereby has a unique potential to approximate efficiently all of its derivatives. One of the consequ
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Cyman, Joanna, and Joanna Raczek. "Application of Doubly Connected Dominating Sets to Safe Rectangular Smart Grids." Energies 15, no. 9 (2022): 2969. http://dx.doi.org/10.3390/en15092969.

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Smart grids, together with the Internet of Things, are considered to be the future of the electric energy world. This is possible through a two-way communication between nodes of the grids and computer processing. It is necessary that the communication is easy and safe, and the distance between a point of demand and supply is short, to reduce the electricity loss. All these requirements should be met at the lowest possible cost. In this paper, we study a two-dimensional rectangular grid graph which is considered to be a model of a smart grid; nodes of the graph represent points and devices of
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Antonio, Yeftanus, Sapto Wahyu Indratno, and Rinovia Simanjuntak. "Cyber Insurance Ratemaking: A Graph Mining Approach." Risks 9, no. 12 (2021): 224. http://dx.doi.org/10.3390/risks9120224.

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Cyber insurance ratemaking (CIRM) is a procedure used to set rates (or prices) for cyber insurance products provided by insurance companies. Rate estimation is a critical issue for cyber insurance products. This problem arises because of the unavailability of actuarial data and the uncertainty of normative standards of cyber risk. Most cyber risk analyses do not consider the connection between Information Communication and Technology (ICT) sources. Recently, a cyber risk model was developed that considered the network structure. However, the analysis of this model remains limited to an unweigh
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MAO, YAPING, ZHIWEI GUO, NAN JIA, and HE LI. "Lineark-Arboricity in Product Networks." Journal of Interconnection Networks 16, no. 03n04 (2016): 1650008. http://dx.doi.org/10.1142/s0219265916500080.

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A linear k-forest is a forest whose components are paths of length at most k. The linear k-arboricity of a graph G, denoted bylak(G), is the least number of linear k-forests needed to decompose G. Recently, Zuo, He, and Xue studied the exact values of the linear(n−1)-arboricity of Cartesian products of various combinations of complete graphs, cycles, complete multipartite graphs. In this paper, for general k we show thatmax{lak(G),lal(H)}≤lamax{k,l}(G□H)≤lak(G)+lal(H)for any two graphs G and H. Denote byG∘H, G×HandG⊠Hthe lexicographic product, direct product and strong product of two graphs G
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Cao, Jian Xiang, Xin Feng, and Zheng Tao Jiang. "On the Graph Parameters of Special Networks." Applied Mechanics and Materials 543-547 (March 2014): 2977–80. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.2977.

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Domination in graphs has become one of the major areas of graph theory with extensive applications in design and analysis of communication networks, computational complexity, and algorithm design. This paper mainly research on domination number and bondage number of the graph, especially, these parameters measure to some extent the robustness of an interconnection network with respect to link failures. By constructing a family of minimum dominating sets we compute the domination number and bondage number of the sun graph.
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