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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, 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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An Invariant of the Graph Isomorphism
2008 IEEE Pacific-Asia Workshop on Computational Intelligence and Industrial Application, 2008The adjacent matrix is defined in this paper for a given graph, and the deformation called dual congruent act on the matrix is discussed. We have shown that any two graphs are isomorphic each other if and only if they having the dual congruent adjacent matrices. So the adjacent matrix of graph is a isomorphic invariants for graph theory.
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On Isomorphisms of Marušič–Scapellato Graphs
Graphs and Combinatorics, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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.
Kaspar Riesen +3 more
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Isomorphisms of \(P_ 4\)-graphs
Australas. J Comb., 1997The \(P_4\)-graph \(P_4(G)\) of a graph \(G\) has all paths on four vertices of \(G\) as its vertices, and two such paths \(P \not= Q\) are adjacent in \(P_4(G)\) if \(P \cup Q\) forms a path on five vertices or a 4-cycle in \(G\). The authors prove the following: (1) If \(G\) and \(H\) are connected graphs with minimum degree at least 3 in which no ...
Xueliang Li 0001, Biao Zhao
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Note on Isomorphisms of Graphs
Journal of the London Mathematical Society, 1967Halin, R., Jung, H. A.
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Graphs with Isomorphic Subgraphs
Journal of the London Mathematical Society, 1972Radjavi, Heydar, Rosenthal, Peter
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A (sub)graph isomorphism algorithm for matching large graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004Mario Vento +2 more
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