On the super connectivity of Kronecker products of graphs

Authors:
Hechao Wang;Erfang Shan;Wei Wang
Affiliations:
Department of Mathematics, Shanghai University, Shanghai 200444, PR China;Department of Mathematics, Shanghai University, Shanghai 200444, PR China;College of Information Engineering, Tarim University, Alar, Xinjiang, 843300, PR China
Venue:
Information Processing Letters
Year:
2012

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Abstract

Let G"1 and G"2 be two graphs. The Kronecker productG"1xG"2 has vertex set V(G"1xG"2)=V(G"1)xV(G"2) and edge set E(G"1xG"2)={(u"1,v"1)(u"2,v"2):u"1u"2@?E(G"1) and v"1v"2@?E(G"2)}. A graph G is super connected, or simply super-@k, if every minimum separating set is the neighbors of a vertex of G, that is, every minimum separating set isolates a vertex. In this paper we show that if G is a graph with @k(G)=@d(G) and K"n(n=3) a complete graph on n vertices, except that G is a complete bipartite graph K"m","m (m=1) and K"n=K"3, then GxK"n is super-@k, where @k(G) and @d(G) are the connectivity and the minimum degree of G, respectively.