Liu, Yan et Yan, Gui Ying, Graphs isomorphic to their maximum matching graphs, Acta mathematica Sinica. English series (Print) , 25(9), 2009, pp. 1507-1516
The maximum matching graph .(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 .(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.