Abstract

A Complementary triple connected substantial independent set is a non-empty subset S $\subset $ V of a graph G$=(V,E)$ if S is a substantial independent set and the induced subgraph $<V-S>$ is triple connected. The Complementary triple connected substantial independence number is the maximum cardinality among all Complementary triple connected substantial independent sets and is indicated by $\beta_{ctcs}$. In this paper, we determine the value of Complementary Triple connected substantial independence number for the lexicographic product of paths and cycles.

Keywords and Phrases

Independence number, Substantial independent set, Complementary triple connected substantial independent set.

A.M.S. subject classification

05C69.

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