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Graphs isomorphic to their maximum matching graphs
Authors:Yan Liu  Gui Ying Yan
Institution:[1]School of Mathematics, South China Normal University, Guangzhou, 510631, P.R. China [2]Academy of Mathematics and Systems Science,Chinese Academy of Science, Beijing, 100190, P.R. China
Abstract:The maximum matching graph ℳ(G) of a graph G is a simple graph whose vertices are the maximum matchings of G and where two maximum matchings are adjacent in ℳ(G) if they differ by exactly one edge. In this paper, we prove that if a graph is isomorphic to its maximum matching graph, then every block of the graph is an odd cycle.
Keywords:isomorphic  maximum matching graph  bipartite graph  factor-critical graph
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