Results 231 to 240 of about 87,870 (251)
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2019
In this article we review some of the most relevant properties related to graph isomorphism and graph components. We start by introducing some concepts related to graph traversal (walks, paths, cycles, circuits), then we introduce two natural concepts related to connectivity: connected and strongly connected components.
Dondi, R, Mauri, G, Zoppis, I
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In this article we review some of the most relevant properties related to graph isomorphism and graph components. We start by introducing some concepts related to graph traversal (walks, paths, cycles, circuits), then we introduce two natural concepts related to connectivity: connected and strongly connected components.
Dondi, R, Mauri, G, Zoppis, I
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Journal of Graph Theory, 1997
The \(P_3\)-graph of a finite simple graph \(G\), denoted \(P_3(G)\), is the graph whose vertices are the 3-vertex paths of \(G\), with adjacency between two such paths whenever their union is a 4-vertex path or a 3-cycle. Note that \(P_k(G)\) can be defined in a similar way, and that these graphs generalize \(P_2(G)\), the line graph of \(G\).
Aldred, R. E. L. +3 more
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The \(P_3\)-graph of a finite simple graph \(G\), denoted \(P_3(G)\), is the graph whose vertices are the 3-vertex paths of \(G\), with adjacency between two such paths whenever their union is a 4-vertex path or a 3-cycle. Note that \(P_k(G)\) can be defined in a similar way, and that these graphs generalize \(P_2(G)\), the line graph of \(G\).
Aldred, R. E. L. +3 more
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2021
The precursor of line graphs as an object of study was in isomorphisms between graphs and automorphisms of graphs. Consider a one-to-one function from the edges of a graph with three edges with a common vertex and a graph with three edges forming a cycle. As shown by Hassler Whitney, this mapping not only preserves adjacency of edges, but these two are
Lowell W. Beineke, Jay S. Bagga
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The precursor of line graphs as an object of study was in isomorphisms between graphs and automorphisms of graphs. Consider a one-to-one function from the edges of a graph with three edges with a common vertex and a graph with three edges forming a cycle. As shown by Hassler Whitney, this mapping not only preserves adjacency of edges, but these two are
Lowell W. Beineke, Jay S. Bagga
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Efficient Suboptimal Graph Isomorphism
2009In the field of structural pattern recognition, graphs provide us with a common and powerful way to represent objects. Yet, one of the main drawbacks of graph representation is that the computation of standard graph similarity measures is exponential in the number of involved nodes. Hence, such computations are feasible for small graphs only.
Riesen, Kaspar +3 more
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Journal of Soviet Mathematics, 1985
This paper concerns algorithms for recognizing the isomorphism of graphs. The introduction gives a survey of works of various authors concerning such algorithms and their computational complexity. Further the paper is divided into four chapters. In the first chapter ''Babai-Lukas theory'' the isomorphism of coloured graphs and of coloured sets is ...
Zemlyachenko, V. N. +2 more
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This paper concerns algorithms for recognizing the isomorphism of graphs. The introduction gives a survey of works of various authors concerning such algorithms and their computational complexity. Further the paper is divided into four chapters. In the first chapter ''Babai-Lukas theory'' the isomorphism of coloured graphs and of coloured sets is ...
Zemlyachenko, V. N. +2 more
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Journal of Graph Theory, 1996
Let \(\Pi_k(G)\) denote the set of all paths on \(k\) vertices of a connected simple graph \(G\). Then the \((k- 1)\)-path graph \(P_k(G)\) of \(G\) has vertex set \(\Pi_k(G)\) and edges joining pairs of vertices that represent two \(P_k\)-paths whose union forms either a path \(P_{k+ 1}\) or a cycle \(C_k\).
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Let \(\Pi_k(G)\) denote the set of all paths on \(k\) vertices of a connected simple graph \(G\). Then the \((k- 1)\)-path graph \(P_k(G)\) of \(G\) has vertex set \(\Pi_k(G)\) and edges joining pairs of vertices that represent two \(P_k\)-paths whose union forms either a path \(P_{k+ 1}\) or a cycle \(C_k\).
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Isomorphism Classes of Graph Bundles
Canadian Journal of Mathematics, 1990AbstractRecently, M. Hofmeister [4] counted all nonisomorphic double coverings of a graph by using its Ζ2 cohomology groups, and J. Kwak and J. Lee [5] did the same work for some finite-fold coverings. In this paper, we give an algebraic characterization of isomorphic graph bundles, from which we get a formula to count all nonisomorphic graph-bundles ...
KWAK, JH, LEE, JE
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Optimum Featurs and Graph Isomorphism
IEEE Transactions on Systems, Man, and Cybernetics, 1974An algorithm is presented to test the graph isomorphism for undirected linear graphs. The graph isomorphism between two or more graphs can be tested by obtaining their optimum codes. The algorithm relabels the nodes of graphs to obtain optimum codes. The optimum code is the code of maximum weight obtained from the upper triangle of the Adjacency matrix
Shah, Yogesh J. +2 more
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Graphs with Isomorphic Subgraphs
Journal of the London Mathematical Society, 1972Radjavi, Heydar, Rosenthal, Peter
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