It is commonly believed that vertex-transitive graphs (and in particular Cayley graphs) tend to contain hamilton cycles. The only known connected vertex-transitive graphs without hamilton cycles are K ...

Cayley graphs provide a powerful and intuitive framework linking group theory with graph theory by representing groups through vertices and edges defined by a generating set. In the realm of finite ...

where the sum runs from 0 to [n/2]. It is known that every matching polynomial has only real roots. See [1,2]. It would be interesting to find a vertex transitive graph whose matching polynomial has a ...

We consider a random object that is associated with both random walks and random media, specifically, the superposition of a configuration of subcritical Bernoulli percolation on an infinite connected ...

For a row-finite graph G with no sinks and in which every loop has an exit, we construct an isomorphism between Ext(C*(G)) and coker(A—I), where A is the vertex matrix of G. If c is the class in Ext(C ...