The only known connected vertex-transitive graphs without hamilton cycles are K 1, K 2, the Petersen graph, the Coxeter graph and two graphs obtained from these by `blowing-up’ each vertex to a ...

More specialised work on graphs admitting vertex-transitive actions by non-abelian simple groups has enhanced our understanding of the interplay between group actions and graph symmetries ...

It would be interesting to find a vertex transitive graph whose matching polynomial has a nonsimple root. Such a graph would not have a hamiltonian path (see [1,2]) and would disprove a conjecture of ...

Various new examples are given as applications, including a description of the Poisson boundary for random walks on vertex-transitive graphs with infinitely many ends and on the Diestel-Leader graphs.

The main results in this paper are about the full coalescence time C of a system of coalescing random walks over a finite graph G. Letting m (G) denote the mean meeting time of two such walkers, we ...