Searching Isomorphic Graphs

  • Anatoly D. Plotnikov East Ukrainian National University, Severodonetsk, Ukraine
Keywords: graph, isomorphism, bijective mapping, isomorphic graphs, algorithm, graph isomorphism problem

Abstract

To determine that two given undirected graphs are isomorphic, we
construct for them auxiliary graphs, using the breadth-first search.
This makes capability to position vertices in each digraph with respect
to each other. If the given graphs are isomorphic, in each of them we
can find such positionally equivalent auxiliary digraphs that have the
same mutual positioning of vertices. Obviously, if the given graphs are
isomorphic, then such equivalent digraphs exist. Proceeding from the
arrangement of vertices in one of the digraphs, we try to determine the
corresponding vertices in another digraph. As a result we develop an
algorithm for constructing a bijective mapping between vertices of the
given graphs if they are isomorphic. The running time of the algorithm
equal toO(n5), where n is the number of graph vertices.

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Published
2017-11-08