ON INDEPENDENCE POLYNOMIALS OF QUOTIENT BASED GRAPHS FOR FINITE ABELIAN GROUPS

ON INDEPENDENCE POLYNOMIALS OF QUOTIENT

Abstract

In this paper we investigated the independence polynomial of quotient based graph {\LARGE${\varphi}$}$_{\scriptscriptstyle H}({ G } )$ of an abelian group $G$ relative to all it's subgroups since a subgroup $H$ of an abelian group is normal . The graph {\LARGE${\varphi}$}$_{\scriptscriptstyle H}({ G } )$ is a graph with condition of adjacency where two distinct elements $x,y \in G$ are adjacent in the graph iff $xy \notin H$. A formula for computing the independence polynomial is obtained.