Some remarks on the Kronecker product of graphs
Information Processing Letters
SIAM Journal on Discrete Mathematics
Computing the bipartite edge frustration of fullerene graphs
Discrete Applied Mathematics
Vertex vulnerability parameters of Kronecker products of complete graphs
Information Processing Letters
Independent sets in tensor graph powers
Journal of Graph Theory
Connectivity of Strong Products of Graphs
Graphs and Combinatorics
A finite automata approach to modeling the cross product of interconnection networks
Mathematical and Computer Modelling: An International Journal
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Let @l(G) be the edge connectivity of G. The direct product of graphs G and H is the graph with vertex set V(GxH)=V(G)xV(H), where two vertices (u"1,v"1) and (u"2,v"2) are adjacent in GxH if u"1u"2@?E(G) and v"1v"2@?E(H). We prove that @l(GxK"n)=min{n(n-1)@l(G),(n-1)@d(G)} for every nontrivial graph G and n=3. We also prove that for almost every pair of graphs G and H with n vertices and edge probability p, GxH is k-connected, where k=O((n/logn)^2).