Note: Connectivity of Kronecker products with complete multipartite graphs

Authors:
Wei Wang;Zhidan Yan
Affiliations:
-;-
Venue:
Discrete Applied Mathematics
Year:
2013

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Some remarks on the Kronecker product of graphs

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Abstract

We study connectivity of a Kronecker product of a general graph G with a complete multipartite graph K"p"""1","p"""2","...","p"""r, where the parameters p"k,k=1,...,r satisfy certain conditions. Precisely, we prove that @k(GxK"p"""1","p"""2","...","p"""r)=min{@?"i"="1^rp"i@k(G),@?"i"="1^r^-^1p"i@d(G)}, where the sequence p"1,p"2,...,p"r satisfies (1) r=3, (2) p"1@?p"2@?...@?p"r, (3) @?"i"="1^r^-^2p"i=p"r"-"1 and (4) @?"i"="1^r^-^1p"i=p"r.