Characterization of perfect matching transitive graphs

Abstract

A graph G is perfect matching transitive, shortly PM-transitive, if for any two perfect matchings M and N of G, there is an automorphism f : V(G) ↦ V(G) such that f_e(M) = N, where f_e(uv) = f(u)f(v). In this paper, the author proposed the definition of PM-transitive, verified PM-transitivity of some symmetric graphs, constructed several families of PM-transitive graphs which are neither vertex-transitive nor edge-transitive, and discussed PM-transitivity of generalized Petersen graphs.