Institute of Mathematics and Informatics Bulgarian Academy of Sciences
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.* The work of this author was supported in part by a grant from IPM (No. 89050111)
