• ADJACENT VERTEX SUM POLYNOMIAL
Abstract
Let G be a graph. The adjacent vertex sum polynomial is defined as S(G, x) = nD(G) – i . xaD(G) – i where D(G) = max {deg v/ v Î G}, nD(G) – i is the sum of the number of adjacent vertices of all the vertices of degree D(G) – i and aD(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.
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