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Journal articles on the topic 'Open graph'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

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1

Jose, Bibin K. "Some New Classes of Open Distance-Pattern Uniform Graphs." International Journal of Combinatorics 2013 (July 24, 2013): 1–7. http://dx.doi.org/10.1155/2013/863439.

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Given an arbitrary nonempty subset M of vertices in a graph G=(V,E), each vertex u in G is associated with the set fMo(u)={d(u,v):v∈M,u≠v} and called its open M-distance-pattern. The graph G is called open distance-pattern uniform (odpu-) graph if there exists a subset M of V(G) such that fMo(u)=fMo(v) for all u,v∈V(G), and M is called an open distance-pattern uniform (odpu-) set of G. The minimum cardinality of an odpu-set in G, if it exists, is called the odpu-number of G and is denoted by od(G). Given some property P, we establish characterization of odpu-graph with property P. In this pape

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Chandrasekar, K. Raja, and S. Saravanakumar. "OPEN PACKING NUMBER FOR SOME CLASSES OF PERFECT GRAPHS." Ural Mathematical Journal 6, no. 2 (2020): 38. http://dx.doi.org/10.15826/umj.2020.2.004.

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Let \(G\) be a graph with the vertex set \(V(G)\). A subset \(S\) of \(V(G)\) is an open packing set of \(G\) if every pair of vertices in \(S\) has no common neighbor in \(G.\) The maximum cardinality of an open packing set of \(G\) is the open packing number of \(G\) and it is denoted by \(\rho^o(G)\). In this paper, the exact values of the open packing numbers for some classes of perfect graphs, such as split graphs, \(\{P_4, C_4\}\)-free graphs, the complement of a bipartite graph, the trestled graph of a perfect graph are obtained.

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Dhamala, Tanka Nath. "Some Discrete Optimization Problems With Hamming and H-Comparability Graphs." Tribhuvan University Journal 27, no. 1-2 (2010): 167–76. http://dx.doi.org/10.3126/tuj.v27i1-2.26400.

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Any H-comparability graph contains a Hamming graph as spanningsubgraph. An acyclic orientation of an H-comparability graph contains an acyclic orientation of the spanning Hamming graph, called sequence graph in the classical open-shop scheduling problem. We formulate different discrete optimization problems on the Hamming graphs and on H-comparability graphs and consider their complexity and relationship. Moreover, we explore the structures of these graphs in the class of irreducible sequences for the open shop problem in this paper.

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4

Miklos, Stanislaw. "Reflexive open mappings on generalized graphs." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 47, no. 3 (1989): 343–49. http://dx.doi.org/10.1017/s1446788700033073.

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AbstractIn this paper we show that a locally connected and locally compact metric image of a generalized graph under a reflexive open mapping is a generalized graph; further, we characterize all acyclic generalized graphs X with the property that any locally one-to-one reflexive open mapping of X into a Hausdorff space is globally one-to-one. Several problems are posed and some examples are given.

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Gharibyan, Aram H., and Petros A. Petrosyan. "ON LOCALLY-BALANCED 2-PARTITIONS OF BIPARTITE GRAPHS." Proceedings of the YSU A: Physical and Mathematical Sciences 54, no. 3 (253) (2020): 137–45. http://dx.doi.org/10.46991/pysu:a/2020.54.3.137.

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A \emph{$2$-partition of a graph $G$} is a function $f:V(G)\rightarrow \{0,1\}$. A $2$-partition $f$ of a graph $G$ is a \emph{locally-balanced with an open neighborhood}, if for every $v\in V(G)$, $\left\vert \vert \{u\in N_{G}(v)\colon\,f(u)=0\}\vert - \vert \{u\in N_{G}(v)\colon\,f(u)=1\}\vert \right\vert\leq 1$. A bipartite graph is \emph{$(a,b)$-biregular} if all vertices in one part have degree $a$ and all vertices in the other part have degree $b$. In this paper we prove that the problem of deciding, if a given graph has a locally-balanced $2$-partition with an open neighborhood is $NP$

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KIYOMI, MASASHI, TOSHIKI SAITOH, and RYUHEI UEHARA. "BIPARTITE PERMUTATION GRAPHS ARE RECONSTRUCTIBLE." Discrete Mathematics, Algorithms and Applications 04, no. 03 (2012): 1250039. http://dx.doi.org/10.1142/s1793830912500395.

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The graph reconstruction conjecture is a long-standing open problem in graph theory. The conjecture has been verified for all graphs with at most 11 vertices. Further, the conjecture has been verified for regular graphs, trees, disconnected graphs, unit interval graphs, separable graphs with no pendant vertex, outer-planar graphs, and unicyclic graphs. We extend the list of graph classes for which the conjecture holds. We give a proof that bipartite permutation graphs are reconstructible.

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ALON, NOGA, and JACOB FOX. "Easily Testable Graph Properties." Combinatorics, Probability and Computing 24, no. 4 (2015): 646–57. http://dx.doi.org/10.1017/s0963548314000765.

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A graph on n vertices is ε-far from a property $\mathcal{P}$ if one has to add or delete from it at least εn2 edges to get a graph satisfying $\mathcal{P}$. A graph property $\mathcal{P}$ is strongly testable if for every fixed ε > 0 it is possible to distinguish, with one-sided error, between graphs satisfying $\mathcal{P}$ and ones that are ε-far from $\mathcal{P}$ by inspecting the induced subgraph on a random subset of at most f(ε) vertices. A property is easily testable if it is strongly testable and the function f is polynomial in 1/ε, otherwise it is hard. We consider the problem of

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Kwun, Young Chel, Hafiz Mutee ur Rehman, Muhammad Yousaf, Waqas Nazeer, and Shin Min Kang. "The Entropy of Weighted Graphs with Atomic Bond Connectivity Edge Weights." Discrete Dynamics in Nature and Society 2018 (December 16, 2018): 1–10. http://dx.doi.org/10.1155/2018/8407032.

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The aim of this report to solve the open problem suggested by Chen et al. We study the graph entropy with ABC edge weights and present bounds of it for connected graphs, regular graphs, complete bipartite graphs, chemical graphs, tree, unicyclic graphs, and star graphs. Moreover, we compute the graph entropy for some families of dendrimers.

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9

HUJDUROVIĆ, ADEMIR. "ON SOME PROPERTIES OF QUASI-DISTANCE-BALANCED GRAPHS." Bulletin of the Australian Mathematical Society 97, no. 2 (2018): 177–84. http://dx.doi.org/10.1017/s000497271700096x.

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For an edge$uv$in a graph$G$,$W_{u,v}^{G}$denotes the set of all vertices of$G$that are closer to$u$than to$v$. A graph$G$is said to bequasi-distance-balancedif there exists a constant$\unicode[STIX]{x1D706}>1$such that$|W_{u,v}^{G}|=\unicode[STIX]{x1D706}^{\pm 1}|W_{v,u}^{G}|$for every pair of adjacent vertices$u$and$v$. The existence of nonbipartite quasi-distance-balanced graphs is an open problem. In this paper we investigate the possible structure of cycles in quasi-distance-balanced graphs and generalise the previously known result that every quasi-distance-balanced graph is triangle-

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10

Benediktovich, V. I. "Analogue of Brauer’s conjecture for the signless Laplacian of cographs." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 56, no. 3 (2020): 310–17. http://dx.doi.org/10.29235/1561-2430-2020-56-3-310-317.

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In this paper, we consider the class of cographs and its subclasses, namely, threshold graphs and anti-regular graphs. In 2011 H. Bai confirmed the Grone – Merris conjecture about the sum of the first k eigenvalues of the Laplacian of an arbitrary graph. As a variation of the Grone – Merris conjecture, A. Brouwer put forward his conjecture about an upper bound for this sum. Although the latter conjecture was confirmed for many graph classes, however, it remains open. By analogy to Brouwer’s conjecture, in 2013 F. Ashraf et al. put forward a conjecture about the sum of k eigenvalues of the sign

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Zheng, Wei, Hajo Broersma, and Ligong Wang. "Toughness, Forbidden Subgraphs and Pancyclicity." Graphs and Combinatorics 37, no. 3 (2021): 839–66. http://dx.doi.org/10.1007/s00373-021-02284-y.

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AbstractMotivated by several conjectures due to Nikoghosyan, in a recent article due to Li et al., the aim was to characterize all possible graphs H such that every 1-tough H-free graph is hamiltonian. The almost complete answer was given there by the conclusion that every proper induced subgraph H of $$K_1\cup P_4$$ K 1 ∪ P 4 can act as a forbidden subgraph to ensure that every 1-tough H-free graph is hamiltonian, and that there is no other forbidden subgraph with this property, except possibly for the graph $$K_1\cup P_4$$ K 1 ∪ P 4 itself. The hamiltonicity of 1-tough $$K_1\cup P_4$$ K 1 ∪

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Moon, Heekyung, Zhanfang Zhao, Jintak Choi, and Sungkook Han. "A novel property graph model for knowledge representation on the Web." International Journal of Engineering & Technology 7, no. 3.33 (2018): 187. http://dx.doi.org/10.14419/ijet.v7i3.33.21010.

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Graphs provide an effective way to represent information and knowledge of real world domains. Resource Description Framework (RDF) model and Labeled Property Graphs (LPG) model are dominant graph data models widely used in Linked Open Data (LOD) and NoSQL databases. Although these graph models have plentiful data modeling capabilities, they reveal some drawbacks to model the complicated structures. This paper proposes a new property graph model called a universal property graph (UPG) that can embrace the capability of both RDF and LPG. This paper explores the core features of UPG and their fun

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13

Grohe, Martin, and Daniel Neuen. "Isomorphism, canonization, and definability for graphs of bounded rank width." Communications of the ACM 64, no. 5 (2021): 98–105. http://dx.doi.org/10.1145/3453943.

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We investigate the interplay between the graph isomorphism problem, logical definability, and structural graph theory on a rich family of dense graph classes: graph classes of bounded rank width. We prove that the combinatorial Weisfeiler-Leman algorithm of dimension (3 k + 4) is a complete isomorphism test for the class of all graphs of rank width at most k. A consequence of our result is the first polynomial time canonization algorithm for graphs of bounded rank width. Our second main result addresses an open problem in descriptive complexity theory: we show that fixed-point logic with count

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14

Ng, Liang S., and Corbin Champion. "The One Universal Graph — a free and open graph database." IOP Conference Series: Materials Science and Engineering 114 (February 2016): 012143. http://dx.doi.org/10.1088/1757-899x/114/1/012143.

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Gharibyan, Aram H., and Petros A. Petrosyan. "LOCALLY-BALANCED $k$-PARTITIONS OF GRAPHS." Proceedings of the YSU A: Physical and Mathematical Sciences 55, no. 2 (255) (2021): 96–112. http://dx.doi.org/10.46991/pysu:a/2021.55.2.096.

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In this paper we generalize locally-balanced $2$-partitions of graphs and introduce a new notion, the locally-balanced $k$-partitions of graphs, defined as follows: a $k$-partition of a graph $G$ is a surjection $f:V(G)\rightarrow \{0,1,\ldots,k-1\}$. A $k$-partition ($k\geq 2$) $f$ of a graph $G$ is a locally-balanced with an open neighborhood, if for every $v\in V(G)$ and any $0\leq i<j\leq k-1$ $$\left\vert \vert \{u\in N_{G}(v)\colon\,f(u)=i\}\vert - \vert \{u\in N_{G}(v)\colon\,f(u)=j\}\vert \right\vert\leq 1.$$ A $k$-partition ($k\geq 2$) $f^{\prime}$ of a graph $G$ is a locally-balan

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16

RAJASEKARAN, SANGUTHEVAR, and VAMSI KUNDETI. "SPECTRUM BASED TECHNIQUES FOR GRAPH ISOMORPHISM." International Journal of Foundations of Computer Science 20, no. 03 (2009): 479–99. http://dx.doi.org/10.1142/s0129054109006693.

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The graph isomorphism problem is to check if two given graphs are isomorphic. Graph isomorphism is a well studied problem and numerous algorithms are available for its solution. In this paper we present algorithms for graph isomorphism that employ the spectra of graphs. An open problem that has fascinated many a scientist is if there exists a polynomial time algorithm for graph isomorphism. Though we do not solve this problem in this paper, the algorithms we present take polynomial time. These algorithms have been tested on a good collection of instances. However, we have not been able to prov

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17

Saenpholphat, Varaporn, and Ping Zhang. "Conditional resolvability in graphs: a survey." International Journal of Mathematics and Mathematical Sciences 2004, no. 38 (2004): 1997–2017. http://dx.doi.org/10.1155/s0161171204311403.

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For an ordered setW={w1,w2,…,wk}of vertices and a vertexvin a connected graphG, the code ofvwith respect toWis thek-vectorcW(v)=(d(v,w1),d(v,w2),…,d(v,wk)), whered(x,y)represents the distance between the verticesxandy. The setWis a resolving set forGif distinct vertices ofGhave distinct codes with respect toW. The minimum cardinality of a resolving set forGis its dimensiondim(G). Many resolving parameters are formed by extending resolving sets to different subjects in graph theory, such as the partition of the vertex set, decomposition and coloring in graphs, or by combining resolving property

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Auer, Sören, and Sanjeet Mann. "Towards an Open Research Knowledge Graph." Serials Librarian 76, no. 1-4 (2018): 35–41. http://dx.doi.org/10.1080/0361526x.2019.1540272.

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19

Min Wan, Yu Wang, E. Bae, Xue-Cheng Tai, and Desheng Wang. "Reconstructing Open Surfaces via Graph-Cuts." IEEE Transactions on Visualization and Computer Graphics 19, no. 2 (2013): 306–18. http://dx.doi.org/10.1109/tvcg.2012.119.

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Mikheenko, Alla, and Mikhail Kolmogorov. "Assembly Graph Browser: interactive visualization of assembly graphs." Bioinformatics 35, no. 18 (2019): 3476–78. http://dx.doi.org/10.1093/bioinformatics/btz072.

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Abstract Summary Currently, most genome assembly projects focus on contigs and scaffolds rather than assembly graphs that provide a more comprehensive representation of an assembly. Since interactive visualization of large assembly graphs remains an open problem, we developed an Assembly Graph Browser (AGB) tool that visualizes large assembly graphs, extending the functionality of previously developed visualization approaches. Assembly Graph Browser includes a number of novel functions including repeat analysis, construction of the contracted assembly graphs (i.e. the graphs obtained by collap

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21

Lanel, G. H. J., H. K. Pallage, J. K. Ratnayake, S. Thevasha, and B. A. K. Welihinda. "A survey on Hamiltonicity in Cayley graphs and digraphs on different groups." Discrete Mathematics, Algorithms and Applications 11, no. 05 (2019): 1930002. http://dx.doi.org/10.1142/s1793830919300029.

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Lovász had posed a question stating whether every connected, vertex-transitive graph has a Hamilton path in 1969. There is a growing interest in solving this longstanding problem and still it remains widely open. In fact, it was known that only five vertex-transitive graphs exist without a Hamiltonian cycle which do not belong to Cayley graphs. A Cayley graph is the subclass of vertex-transitive graph, and in view of the Lovász conjecture, the attention has focused more toward the Hamiltonicity of Cayley graphs. This survey will describe the current status of the search for Hamiltonian cycles

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Ronzhin, Folmer, Maria, et al. "Kadaster Knowledge Graph: Beyond the Fifth Star of Open Data." Information 10, no. 10 (2019): 310. http://dx.doi.org/10.3390/info10100310.

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After more than a decade, the supply-driven approach to publishing public (open) data has resulted in an ever-growing number of data silos. Hundreds of thousands of datasets have been catalogued and can be accessed at data portals at different administrative levels. However, usually, users do not think in terms of datasets when they search for information. Instead, they are interested in information that is most likely scattered across several datasets. In the world of proprietary in-company data, organizations invest heavily in connecting data in knowledge graphs and/or store data in data lak

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Noja, Diego. "Nonlinear Schrödinger equation on graphs: recent results and open problems." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2007 (2014): 20130002. http://dx.doi.org/10.1098/rsta.2013.0002.

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In this paper, an introduction to the new subject of nonlinear dispersive Hamiltonian equations on graphs is given. The focus is on recently established properties of solutions in the case of the nonlinear Schrödinger (NLS) equation. Special consideration is given to the existence and behaviour of solitary solutions. Two subjects are discussed in some detail concerning the NLS equation on a star graph: the standing waves of the NLS equation on a graph with a δ interaction at the vertex, and the scattering of fast solitons through a Y-junction in the cubic case. The emphasis is on a description

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Linial, Nathan. "Local-Global Phenomena in Graphs." Combinatorics, Probability and Computing 2, no. 4 (1993): 491–503. http://dx.doi.org/10.1017/s0963548300000857.

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This is a survey of a number of recent papers dealing with graphs from a geometric perspective. The main theme of these studies is the relationship between graph properties that are local in nature, and global graph parameters. Connections with the theory of distributed computing are pointed out and many open problems are presented.

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Raza, Hassan. "Computing Open Locating-Dominating Number of Some Rotationally-Symmetric Graphs." Mathematics 9, no. 12 (2021): 1415. http://dx.doi.org/10.3390/math9121415.

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Location detection is studied for many scenarios, such as pointing out the flaws in multiprocessors, invaders in buildings and facilities, and utilizing wireless sensor networks for monitoring environmental processes. The system or structure can be illustrated as a graph in each of these applications. Sensors strategically placed at a subset of vertices can determine and identify irregularities within the network. The open locating-dominating set S of a graph G=(V,E) is the set of vertices that dominates G, and for any i,j∈ V(G) N(i)∩S≠N(j)∩S is satisfied. The set S is called the OLD-set of G.

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Formanowicz, Piotr, and Krzysztof Tanaś. "A survey of graph coloring - its types, methods and applications." Foundations of Computing and Decision Sciences 37, no. 3 (2012): 223–38. http://dx.doi.org/10.2478/v10209-011-0012-y.

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Abstract Graph coloring is one of the best known, popular and extensively researched subject in the field of graph theory, having many applications and conjectures, which are still open and studied by various mathematicians and computer scientists along the world. In this paper we present a survey of graph coloring as an important subfield of graph theory, describing various methods of the coloring, and a list of problems and conjectures associated with them. Lastly, we turn our attention to cubic graphs, a class of graphs, which has been found to be very interesting to study and color. A brie

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Božović, Dragana, and Iztok Peterin. "Efficient Open Domination in Digraph Products." Mathematics 8, no. 4 (2020): 496. http://dx.doi.org/10.3390/math8040496.

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A digraph D is an efficient open domination digraph if there exists a subset S of V ( D ) for which the open out-neighborhoods centered in the vertices of S form a partition of V ( D ) . In this work we deal with the efficient open domination digraphs among four standard products of digraphs. We present a method for constructing the efficient open domination Cartesian product of digraphs with one fixed factor. In particular, we characterize those for which the first factor has an underlying graph that is a path, a cycle or a star. We also characterize the efficient open domination strong produ

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Kuhlmann, Marco, and Stephan Oepen. "Towards a Catalogue of Linguistic Graph Banks." Computational Linguistics 42, no. 4 (2016): 819–27. http://dx.doi.org/10.1162/coli_a_00268.

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Graphs exceeding the formal complexity of rooted trees are of growing relevance to much NLP research. Although formally well understood in graph theory, there is substantial variation in the types of linguistic graphs, as well as in the interpretation of various structural properties. To provide a common terminology and transparent statistics across different collections of graphs in NLP, we propose to establish a shared community resource with an open-source reference implementation for common statistics.

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SZÉKELY, ZOLTÁN. "COMPUTATIONAL COMPLEXITY OF THE FINITE ALGEBRA MEMBERSHIP PROBLEM FOR VARIETIES." International Journal of Algebra and Computation 12, no. 06 (2002): 811–23. http://dx.doi.org/10.1142/s0218196702001085.

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We exhibit finite algebras each generating a variety with NP-complete finite algebra membership problem. The smallest of these algebras is the flat graph algebra belonging to the tetrahedral graph, a graph of 6 vertices obtained by cutting and spreading out the surface of a tetrahedron on the plane. The sequence of graphs we use to build up our flat graph algebras is similar to the sequence exhibited by Wheeler in [36] , 1979, to describe the first order theory of k-colorable graphs. Graph algebras were introduced by Shallon in [34] , 1979, and investigated, among others, by Baker, McNulty and

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Ashrafi, Ali, and Fatemeh Koorepazan-Moftakhar. "On normal graph of a finite group." Filomat 32, no. 11 (2018): 4047–59. http://dx.doi.org/10.2298/fil1811047a.

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Suppose G is a finite group and C(G) denotes the set of all conjugacy classes of G. The normal graph of G, N(G), is a finite simple graph such that V(N(G)) = C(G). Two conjugacy classes A and B in C(G) are adjacent if and only if there is a proper normal subgroup N such that A U B ? N. The aim of this paper is to study the normal graph of a finite group G. It is proved, among other things, that the groups with identical character table have isomorphic normal graphs and so this new graph associated to a group has good relationship by its group structure. The normal graphs of some classes of fin

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Chen, Yin, Baoyindureng Wu, and Xinhui An. "Wiener Index of Graphs with Radius Two." ISRN Combinatorics 2013 (March 3, 2013): 1–5. http://dx.doi.org/10.1155/2013/906756.

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The Wiener index of a graph is the sum of the distances between all pairs of vertices. It has been one of main descriptors that correlate a chemical compound's molecular graph with experimentally gathered data regarding the compound's characteristics. We characterize graphs with the maximum Wiener index among all graphs of order . with radius two. In addition, we pose a conjecture concerning the minimum Wiener index of graphs with given radius. If this conjecture is true, it will be able to answer an open question by You and Liu (2011).

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El Moussawi, Adnan, Nacera Bennacer Seghouani, and Francesca Bugiotti. "BGRAP: Balanced GRAph Partitioning Algorithm for Large Graphs." Journal of Data Intelligence 2, no. 2 (2021): 116–35. http://dx.doi.org/10.26421/jdi2.2-2.

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The definition of effective strategies for graph partitioning is a major challenge in distributed environments since an effective graph partitioning allows to considerably improve the performance of large graph data analytics computations. In this paper, we propose a multi-objective and scalable Balanced GRAph Partitioning (\algo) algorithm, based on Label Propagation (LP) approach, to produce balanced graph partitions. \algo defines a new efficient initialization procedure and different objective functions to deal with either vertex or edge balance constraints while considering edge direction

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Mete, Filiz, Serife Buyukkose, Ozlem Cakir, and Ummugulsum Candeger. "Graphic representation of open and distance education history." Global Journal of Information Technology: Emerging Technologies 7, no. 3 (2017): 92–98. http://dx.doi.org/10.18844/gjit.v7i3.2831.

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Nowadays, learning and instruction take place independent of time and space through the distance education system,wherein courses are conducted completely online through network technologies using interactive video -based instructional materials. This study examines the open and distance education system that was a part of the history of education in the Turkish republic first at universities, and then in high sch ools and secondary schools. It is aimed to narrate the history of open and distance education using graph theory trees in order to provide a better understanding of this process. Wit

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Bielawski, Roger. "A selection theorem for open-graph multifunctions." Fundamenta Mathematicae 133, no. 2 (1989): 97–100. http://dx.doi.org/10.4064/fm-133-2-97-100.

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Germina, K. A., and P. T. Marykutty. "Open Distance Pattern Coloring of a Graph." Journal of Fuzzy Set Valued Analysis 2012 (2012): 1–8. http://dx.doi.org/10.5899/2012/jfsva-00144.

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S, Balamurugan, Anitha M, Karnan C, and Palanikumar P. "Open Support of a Graph under Multiplication." International Journal of Mathematics Trends and Technology 65, no. 5 (2019): 134–38. http://dx.doi.org/10.14445/22315373/ijmtt-v65i5p521.

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Veettil, Ragi Puthan, and Ramakrishnan T.V. "The open hub number of a graph." Malaya Journal of Matematik 8, no. 4 (2020): 1375–77. http://dx.doi.org/10.26637/mjm0804/0006.

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Lee, Giho, and Incheol Kim. "Open Domain Question Answering using Knowledge Graph." Journal of KIISE 47, no. 9 (2020): 853–62. http://dx.doi.org/10.5626/jok.2020.47.9.853.

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Saravanakumar, S., A. Anitha, and I. Sahul Hamid. "Open packing bondage number of a graph." Discrete Mathematics, Algorithms and Applications 11, no. 05 (2019): 1950051. http://dx.doi.org/10.1142/s1793830919500514.

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In a graph [Formula: see text], a set [Formula: see text] is said to be an open packing set if no two vertices of [Formula: see text] have a common neighbor in [Formula: see text] The maximum cardinality of an open packing set is called the open packing number and is denoted by [Formula: see text]. The open packing bondage number of a graph [Formula: see text], denoted by [Formula: see text], is the cardinality of the smallest set of edges [Formula: see text] such that [Formula: see text]. In this paper, we initiate a study on this parameter.

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Hamid, I. Sahul, and S. Saravanakumar. "Open packing saturation number of a graph." Asian-European Journal of Mathematics 10, no. 02 (2016): 1750033. http://dx.doi.org/10.1142/s1793557117500334.

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In a graph [Formula: see text], a non-empty set [Formula: see text] is said to be an open packing set if no two vertices of [Formula: see text] have a common neighbor in [Formula: see text] Let [Formula: see text] and let [Formula: see text] denote the maximum cardinality of an open packing set in [Formula: see text] which contains [Formula: see text]. Then [Formula: see text] is called the open packing saturation number of [Formula: see text]. In this paper, we initiate a study on this parameter.

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Payne, Karen. "Graph Theory and Open-space Network Design." Landscape Research 27, no. 2 (2002): 167–79. http://dx.doi.org/10.1080/01426390220128640.

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Son, Jiseong, Chul-Su Lim, Hyoung-Seop Shim, and Ji-Sun Kang. "Development of Knowledge Graph for Data Management Related to Flooding Disasters Using Open Data." Future Internet 13, no. 5 (2021): 124. http://dx.doi.org/10.3390/fi13050124.

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Despite the development of various technologies and systems using artificial intelligence (AI) to solve problems related to disasters, difficult challenges are still being encountered. Data are the foundation to solving diverse disaster problems using AI, big data analysis, and so on. Therefore, we must focus on these various data. Disaster data depend on the domain by disaster type and include heterogeneous data and lack interoperability. In particular, in the case of open data related to disasters, there are several issues, where the source and format of data are different because various da

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PROCESI, C. "THE ENERGY GRAPH OF THE NONLINEAR SCHRÖDINGER EQUATION, OPEN PROBLEMS." International Journal of Algebra and Computation 23, no. 04 (2013): 943–62. http://dx.doi.org/10.1142/s021819671340016x.

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We discuss some combinatorial and algebraic problems which have arisen from the study of the nonlinear Schrödinger equation. In particular we discuss a combinatorial graph, which we call energy graph associated to a Cayley graph. Some important features of normal forms are hidden into properties of this graph. Some of these properties are at the moment only conjectural and we point out the state of the art.

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LIN, YAW-LING, and STEVEN S. SKIENA. "COMPLEXITY ASPECTS OF VISIBILITY GRAPHS." International Journal of Computational Geometry & Applications 05, no. 03 (1995): 289–312. http://dx.doi.org/10.1142/s0218195995000179.

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In this paper, we consider two distinct problems related to complexity aspects of the visibility graphs of simple polygons. Recognizing visibility graphs is a long-standing open problem. It is not even known whether visibility graph recognition is in NP. That visibility graph recognition is in NP would be established if we could demonstrate that any n vertex visibility graph is realized by a polygon which can be drawn on an exponentially-sized grid. This motivates a study of the area requirements for realizing visibility graphs. In this paper, we prove: • Θ(n3) area is necessary and sufficient

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Peterin, Iztok. "The complexity of open k-monopolies in graphs for negative k." Opuscula Mathematica 39, no. 3 (2019): 425–31. http://dx.doi.org/10.7494/opmath.2019.39.3.425.

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Let \(G\) be a graph with vertex set \(V(G)\), \(\delta(G)\) minimum degree of \(G\) and \(k\in\left\{1-\left\lceil\frac{\delta(G)}{2}\right\rceil,\ldots ,\left\lfloor \frac{\delta(G)}{2}\right\rfloor\right\}\). Given a nonempty set \(M\subseteq V(G)\) a vertex \(v\) of \(G\) is said to be \(k\)-controlled by \(M\) if \(\delta_M(v)\ge\frac{\delta_{V(G)}(v)}{2}+k\) where \(\delta_M(v)\) represents the number of neighbors of \(v\) in \(M\). The set \(M\) is called an open \(k\)-monopoly for \(G\) if it \(k\)-controls every vertex \(v\) of \(G\). In this short note we prove that the problem of co

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Makarov, Ilya, Dmitrii Kiselev, Nikita Nikitinsky, and Lovro Subelj. "Survey on graph embeddings and their applications to machine learning problems on graphs." PeerJ Computer Science 7 (February 4, 2021): e357. http://dx.doi.org/10.7717/peerj-cs.357.

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Dealing with relational data always required significant computational resources, domain expertise and task-dependent feature engineering to incorporate structural information into a predictive model. Nowadays, a family of automated graph feature engineering techniques has been proposed in different streams of literature. So-called graph embeddings provide a powerful tool to construct vectorized feature spaces for graphs and their components, such as nodes, edges and subgraphs under preserving inner graph properties. Using the constructed feature spaces, many machine learning problems on graph

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Shah, Haseeb, Johannes Villmow, Adrian Ulges, Ulrich Schwanecke, and Faisal Shafait. "An Open-World Extension to Knowledge Graph Completion Models." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 3044–51. http://dx.doi.org/10.1609/aaai.v33i01.33013044.

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We present a novel extension to embedding-based knowledge graph completion models which enables them to perform open-world link prediction, i.e. to predict facts for entities unseen in training based on their textual description. Our model combines a regular link prediction model learned from a knowledge graph with word embeddings learned from a textual corpus. After training both independently, we learn a transformation to map the embeddings of an entity’s name and description to the graph-based embedding space.In experiments on several datasets including FB20k, DBPedia50k and our new dataset

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Duong, Linh, Brenda K. Kroschel, Michael Riddell, Kevin N. Vander Meulen, and Adam Van Tuyl. "Maximum nullity and zero forcing of circulant graphs." Special Matrices 8, no. 1 (2020): 221–34. http://dx.doi.org/10.1515/spma-2020-0106.

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AbstractThe zero forcing number of a graph has been applied to communication complexity, electrical power grid monitoring, and some inverse eigenvalue problems. It is well-known that the zero forcing number of a graph provides a lower bound on the minimum rank of a graph. In this paper we bound and characterize the zero forcing number of various circulant graphs, including families of bipartite circulants, as well as all cubic circulants. We extend the definition of the Möbius ladder to a type of torus product to obtain bounds on the minimum rank and the maximum nullity on these products. We o

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Rousseau, C. C., and S. E. Speed. "Mixed Ramsey Numbers Revisited." Combinatorics, Probability and Computing 12, no. 5-6 (2003): 653–60. http://dx.doi.org/10.1017/s0963548303005704.

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Given a graph Hwith no isolates, the (generalized) mixed Ramsey number is the smallest integer r such that every H-free graph of order r contains an m-element irredundant set. We consider some questions concerning the asymptotic behaviour of this number (i) with H fixed and , (ii) with m fixed and a sequence of dense graphs, in particular for the sequence . Open problems are mentioned throughout the paper.

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IBARRA, LOUIS, and DANA RICHARDS. "TREE OPEN EAR DECOMPOSITION IN PARALLEL GRAPH ALGORITHMS." Parallel Processing Letters 05, no. 02 (1995): 129–38. http://dx.doi.org/10.1142/s0129626495000114.

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Tree open ear decomposition has been proposed as a potentially useful technique in parallel graph algorithms. We present an efficient parallel algorithm implementing depth-first search in a graph, given its tree open ear decomposition. The algorithm runs in O( log n) time with O(m) processors on the CREW PRAM, where m is the number of edges in the graph. We also show that the problem of computing such a decomposition is NP-complete, demonstrating the limited utility of the technique.

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