On Arc Connectivity of Direct-Product Digraphs

Various product operations are employed for constructing larger networks from smaller ones, among which direct-product operation is the most frequently employed one. The direct product of two graphs G1 andG2, denoted byG1×G2, is defined on vertex set V G1 ×V G2 , where two vertices x1, x2 and y1, y2 are adjacent to each other in G1 × G2 if and only if x1y1 ∈ E G1 and x2y2 ∈ E G2 . Other names for direct product are tensor product, categorical product, Kronecker product, cardinal product, relational product, and weak direct product 1 . Some basic connectivity properties of direct-product graphs are presented in 2, 3 and elsewhere. Specially, the authors characterize connected product graphs by presenting the following Theorem 1.1 in 1 ; an explicit expression of the connectivity of a direct-product graph is presented in 4 .