• ADJACENT VERTEX SUM POLYNOMIAL

Abstract

Let G be a graph. The adjacent vertex sum polynomial is defined as S(G, x) = n_{D(G) – i} . x^{aD(G) – i} where D(G) = max {deg v/ v Î G}, n_{D(G) – i} is the sum of the number of adjacent vertices of all the vertices of  degree D(G) – i and a_{D(G) – i} is the sum of the degree of adjacent vertices of all the vertices of degree D(G) – i. In this paper I find the adjacent vertex sum polynomial of Cyclic graph, Complete graph, Generalized Peterson graph, Complete bipartite graph, Anti regular graph, Gear graph, Barbell graph and Book graph.