Group connectivity of semistrong product of graphs

For a 2-edge-connected graph G, the group connectivity number of G is defined as Λg(G) = min{k : G is A-connected for every abelian group with |A| ≥ k}. Let G •H denote the semistrong product of two graphs G and H. In this paper, we extend the result of Yan et al. [Int. J. Algebra 4 (2010), 1185–1200] on group connectivity in Cartesian product of graphs to semistrong products and make a slightly stronger conclusion: Λg(G•H) ≤ 5 for two nontrivial connected simple graphs G and H, where equality holds if and only if either G •H ∼= T •K2, where T is a tree, or G •H ∼= K2 •K1,m, where m ≥ 2.