Independent sets in direct products of vertex-transitive graphs

Authors:
Huajun Zhang
Affiliations:
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, PR China and Department of Mathematics, Shanghai Normal University, Shanghai 200234, PR China
Venue:
Journal of Combinatorial Theory Series B
Year:
2012

Citing 10
Cited 1

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Abstract

The direct product GxH of graphs G and H is defined byV(GxH)=V(G)xV(H) andE(GxH)={[(u"1,v"1),(u"2,v"2)]:(u"1,u"2)@?E(G) and(v"1,v"2)@?E(H)}. In this paper, we will prove that@a(GxH)=max{@a(G)|H|,@a(H)|G|} holds for all vertex-transitive graphs G and H, which provides an affirmative answer to a problem posed by Tardif (1998) [11]. Furthermore, the structure of all maximum independent sets of GxH is determined.