Bounded edge-connectivity and edge-persistence of Cartesian product of graphs

Authors:
You Lu;Jun-Ming Xu;Xin-Min Hou
Affiliations:
Department of Mathematics, University of Science and Technology of China, Hefei, 230026, China;Department of Mathematics, University of Science and Technology of China, Hefei, 230026, China;Department of Mathematics, University of Science and Technology of China, Hefei, 230026, China
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

The bounded edge-connectivity @l"k(G) of a connected graph G with respect to k(=d(G)) is the minimum number of edges in G whose deletion from G results in a subgraph with diameter larger than k and the edge-persistence D^+(G) is defined as @l"d"("G")(G), where d(G) is the diameter of G. This paper considers the Cartesian product G"1xG"2, shows @l"k"""1"+"k"""2(G"1xG"2)=@l"k"""1(G"1)+@l"k"""2(G"2) for k"1=2 and k"2=2, and determines the exact values of D^+(G) for G=C"nxP"m, C"nxC"m, Q"nxP"m and Q"nxC"m.