For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

We investigate the computational complexity of graph primality testing problem with respect to direct product (also known as Kronecker, cardinal or tensor product). In [1] Imrich proves that both and a unique prime factorization can be determined in polynomial time for (finite) connected nonbipartite graphs. The author states an open how results on nonbipartite, graphs extend bipartite disconne...

If each minimal dominating set in a graph is minimum set, then the called well-dominated. Since seminal paper on well-dominated graphs appeared 1988, structure of from several restricted classes has been studied. In this we give complete characterization nontrivial direct products that are We prove if strong product well-dominated, both its factors When one graph, other factor being also suffic...

A vertex-cut S is called a super if G − disconnected and it contains no isolated vertices. The super-connectivity , κ ′, the minimum cardinality over all vertex-cuts. This article provides bounds for connectivity of direct product an arbitrary graph complete K n . Among other results, we show that non-complete with girth( ) = 3 ′( ∞, then × ≤ min{ mn 6, m ( 1) + 5, 5 8}, where | V )|