The Eccentric Connectivity Polynomial of Some Graph Operations

Authors

  • Ali Reza Ashrafi
  • Modjtaba Ghorbani
  • Mohammad Ali Hossein-Zadeh

DOI:

https://doi.org/10.55630/sjc.2011.5.101-116

Keywords:

Graph Operation, Topological Index, Eccentric Connectivity Polynomial

Abstract

The eccentric connectivity index of a graph G, ξ^C, was proposed by Sharma, Goswami and Madan. It is defined as ξ^C(G) = ∑ u ∈ V(G) degG(u)εG(u), where degG(u) denotes the degree of the vertex x in G and εG(u) = Max{d(u, x) | x ∈ V (G)}. The eccentric connectivity polynomial is a polynomial version of this topological index. In this paper, exact formulas for the eccentric connectivity polynomial of Cartesian product, symmetric difference, disjunction and join of graphs are presented.

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Published

2011-07-19

Issue

Section

Articles