2018•Electronic Journal of Graph Theory and ApplicationsOpen access

Characterization of perfect matching transitive graphs

Ju Zhou

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 ( u v ) = 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.

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Key concepts: Transitive relation, Combinatorics, Transitive reduction, Mathematics, Transitive closure, Vertex (graph theory), Graph, Symmetric graph