The Eccentric Connectivity Polynomial of some Graph Operations

By Ali Reza Ashrafi, Modjtaba Ghorbani, Mohammad Ali Hosseinzadeh. Serdica Journal of Computing, 2011

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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.

Subfields: Computational Theory and Mathematics, Geometry and Topology

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