Research On The PM-compact Property Of Several Types Of Graphs

The perfect matching graph of graph G is the graph gotten by letting each perfect matching of G be a vertex and two vertices are adjacent if and only if the symmetric difference of those two perfect matchings is a cycle,denoted it by PM(G).If PM(G)is a complete graph,we call G is perfect matching compact,or PM-compact for short.In this paper,we research on the PM-compact property of several types of graphs.In the first chapter,we introduce the research background and the research progress of the PM-compact graphs.In the second chapter,we introduce some basic terms and the lemmas.In the third chapter,we research on the PM-compact property of a class of the Cartesian product graphs,all PM-compact graphs in the class of Cartesian product graphs are characterized.In the fourth chapter,we research on the PM-compact property of a class of the Circular graphs,all PM-compact graphs in the class of Circular graphs are characterized.In the fifth chapter,all PM-compact graphs in the class ofK₄ augment graphs are characterized.In the sixth chapter,all PM-compact graphs in the Generalized Petersen graphs are characterized.