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Graph isomorphism completeness for chordal bipartite graphs and strongly chordal graphs [PDF]
Discrete Applied Mathematics, 2005 This paper deal with the graph isomorphism (GI) problem for two graph classes: chordal bipartite graphs and strongly chrdal graphs. It is known that GI problem is GI complete for some special graph classes including regular graphs, bipartite graphs ...
Ryuhei Uehara
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Improved random graph isomorphism
Journal of Discrete Algorithms, 2008 Canonical labeling of a graph consists of assigning a unique label to each vertex such that the labels are invariant under isomorphism. Such a labeling can be used to solve the graph isomorphism problem.
Gopal Pandurangan
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New Mathematics and Natural Computation, 2023
The soft set theory provides a flexible framework for dealing with uncertain and imprecise information that is not adequately handled by classical set theory. The notion of a soft set was utilized to introduce the concept of a soft graph, which enables the generation of various representations of a relation represented by a graph through ...
Rajesh K. Thumbakara +2 more
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The soft set theory provides a flexible framework for dealing with uncertain and imprecise information that is not adequately handled by classical set theory. The notion of a soft set was utilized to introduce the concept of a soft graph, which enables the generation of various representations of a relation represented by a graph through ...
Rajesh K. Thumbakara +2 more
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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 \(G\).
Robert E. L. Aldred +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 \(G\).
Robert E. L. Aldred +3 more
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Communications of the ACM, 2020
Exploring the theoretical and practical aspects of the graph isomorphism problem.
Martin Grohe, Pascal Schweitzer
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Exploring the theoretical and practical aspects of the graph isomorphism problem.
Martin Grohe, Pascal Schweitzer
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On the cycle‐isomorphism of graphs
Journal of Graph Theory, 1991AbstractThis paper considers conditions ensuring that cycle‐isomorphic graphs are isomorphic. Graphs of connectivity ⩾ 2 that have no loops were studied in [2] and [4]. Here we characterize all graphs G of connectivity 1 such that every graph that is cycle‐isomorphic to G is also isomorphic to G.
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Journal of Graph Theory, 1977
AbstractThe graph isomorphism problem—to devise a good algorithm for determining if two graphs are isomorphic—is of considerable practical importance, and is also of theoretical interest due to its relationship to the concept of NP‐completeness. No efficient (i.e., polynomial‐bound) algorithm for graph isomorphism is known, and it has been conjectured ...
Ronald C. Read, Derek G. Corneil
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AbstractThe graph isomorphism problem—to devise a good algorithm for determining if two graphs are isomorphic—is of considerable practical importance, and is also of theoretical interest due to its relationship to the concept of NP‐completeness. No efficient (i.e., polynomial‐bound) algorithm for graph isomorphism is known, and it has been conjectured ...
Ronald C. Read, Derek G. Corneil
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On the hardness of graph isomorphism
Proceedings 41st Annual Symposium on Foundations of Computer Science, 2002Summary: We show that the graph isomorphism problem is hard under DLOGTIME uniform AC{\(^0\)} many-one reductions for the complexity classes NL, PL (probabilistic logarithmic space) for every logarithmic space modular class {Mod}\(_k\)L and for the class DET of problems NC{\(^1\)} reducible to the determinant.
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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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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
Yogesh J. Shah +2 more
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