Generalized Cayley graphs
The autors introduce the concept of generalized Cayley graph. The main result is that if \(X\) is a graph, \(B(X)\) its double covering then \(B(X)\) is a Cayley graph if and only if \(X\) is a generalized Cayley graph. Another result is that a generalized Cayley graph that is stable is a Cayley graph. Furthermore a construction is given of a family of generalized Cayley graphs that are not vertex transitive and therefore not Cayley graphs. This implies that they are unstable. Moreover it is proved that the constructed graphs are connected and therefore they are nontrivial unstable graphs.
scientific article; zbMATH DE number 64637