Perfect matching transitivity of circulant graphs. - Isaac Armando Reiter; Ju Zhou (Electronic Journal of Graph Theory and Applications (EJGTA), 2022)
A graph G is perfect matching transitive, shortly PM-transitive, if for any two perfect matchings M1 and M2 of G, there is an automorphism f : V(G)↦V(G) such that fe(M1)=M2, where fe(uv)=f(u)f(v). In this paper, the authors completely characterize the perfect matching transitivity of circulant graphs of order less than or equal to 10.