Let y(G) be the domination number of a graph G and let G U H denote the Cartesian product of graphs G and H. We prove that y(X) = (nr= ,nr)/(2m + l), where X = C1 0 CZ 0 ... 0 C, and all nt = ICkIr 1â€¦ (More)

Let X be a connected locally finite transitive graph with polynomial growth. We show that there exist infinitely many finite graphs Y1, Y2 .... such that X is a covering graph of each of these graphsâ€¦ (More)

X(V, E) denotes a graph with vertex-set V(X) and edge-set E(X). Graphs considered in this paper contain neither loops nor mu!tiple edges, AUT(X) denotes the automorphism group of X. We say a subgroupâ€¦ (More)

In an in nite digraph D an edge e is reachable from an edge e if there exists an alternating walk in D whose initial and terminal edges are e and e Reachability is an equivalence relation and if D isâ€¦ (More)

A directed Cayley graph X is called a digraphical regular representation (DRR) of a group G if the automorphism group of X acts regularly on X . Let S be a finite generating set of the infiniteâ€¦ (More)

Let P be a double ray in an infinite graph X, and let d and dP denote the distance functions in X and in P respectively. One calls P a geodesic if d(x, y)=dP(x, y), for all vertices x and y in P. Weâ€¦ (More)

The graphs considered in this paper are undirected connected locally finite graphs without loops or multiple edges. The symbols V(1 ), E(1 ), and Aut(1 ) will denote, respectively, the vertex set,â€¦ (More)

Let D be a locally finite, connected, 1-arc transitive digraph. It is shown that the reachability relation is not universal inD providedthat the stabilizer of an edge satisfies certain conditionsâ€¦ (More)