The independence polynomial of n-th central graph of dihedral groups

Abstract

An independent set of a graph is a set of pairwise non-adjacent vertices while the independence number is the maximum cardinality of an independent set in the graph. The independence polynomial of a graph is defined as a polynomial in which the coefficient is the number of the independent set in the graph. Meanwhile, a graph of a group G is called n-th central if the vertices are elements of G and two distinct vertices are adjacent if they are elements in the n-th term of the upper central series of G. In this research, the independence polynomial of the n-th central graph is found for some dihedral groups.