Energy of Complement of Stars

Abstract

Abstract. The concept of energy of a graph was put forward by I. Gutman in (1978). The characteristic polynomial of a graph G with p vertices is defined as φ(G : λ) = det(λI − A(G), where A(G) is the adjacency matrix of G and I is the unit matrix. The roots of the characteristic equation φ(G : λ) = 0, denoted by λ 1 , λ 2 , . . . , λp are the eigenvalues of G. The energy E = E(G) of a graph G is defined asThe graphs with large number of edges are referred as graph representation of inorganic clusters, called as cluster graphs. In this paper we obtain the characteristic polynomial and energy of class of cluster graphs which are termed as complement of stars.