On the harmonic index and harmonic polynomial of Caterpillars with diameter four

Document Type: Research Paper

Authors

Department of Mathematics, Yazd University, 89195741, Yazd, Iran

Abstract

The harmonic index H(G) , of a graph G is defined as the sum of weights 2/(deg(u)+deg(v)) of all edges in E(G), where deg (u) denotes the degree of a vertex u in V(G). In this paper we define the harmonic polynomial of G. We present explicit formula for the values of harmonic polynomial for several families of specific graphs and we find the lower and upper bound for harmonic index in Caterpillars withf diameter 4.

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