This paper concerns finite, edge-transitive direct and strong products, as well as infinite weak Cartesian products. We prove that the direct product of two connected, non-bipartite graphs is edge-transitive if and only if both factors are edgetransitive and at least one is arc-transitive, or one factor is edge-transitive and the other is a complete graph with loops at each vertex. Also, a stro...

A subgroup of the automorphism group a graph acts half-arc-transitively on if it transitively vertex-set and edge-set but not arc-set graph. If full half-arc-transitively, is said to be half-arc-transitive. In 1994 Gardiner Praeger introduced two families tetravalent arc-transitive graphs, called C±1 C±ε that play prominent role in characterization graphs admitting an automorphisms with normal ...

We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...

Shortest transitive edge relation presents an alternative to transitive closure relation for answering a class of complex biological queries that requires connectivity information but not the full transitive closure. A biological querie such “ find each downstream protein interacting with glutamine synthetase using five or fewer interactions ” does not require transitive closure. Shortest trans...

We study the class of edge-transitive graphs of square-free order and valency at most k. It is shown that, except for a few special families of graphs, only finitely many members in this class are basic (namely, not a normal multicover of another member). Using this result, we determine the automorphism groups of locally primitive arc-transitive graphs with square-free order.

Slovenija Abstract A vertex-transitive graph is said to be 1 2-transitive if its automor-phism group is vertex and edge but not arc-transitive. Some recent results on 1 2-transitive graphs are given, a few open problems proposed , and possible directions in the research of the structure of these graphs discussed. 1 In the beginning Throughout this paper graphs are simple and, unless otherwise s...

Recent work of Lazarovich provides necessary and sufficient conditions on a graph L for there to exist a unique simply-connected (k, L)-complex. The two conditions are symmetry properties of the graph, namely star-transitivity and st(edge)-transitivity. In this paper we investigate star-transitive and st(edge)-transitive graphs by studying the structure of the vertex and edge stabilisers of suc...