Geodesic
The Eccentric Connectivity Polynomial of some Graph Operations
Serdica Journal of Computing, Tome 5 (2011) no. 2, pp. 101-116

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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.
Keywords: Graph Operation, Topological Index, Eccentric Connectivity Polynomial 
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Ashrafi, A.; Ghorbani, M.; Hossein-Zadeh, M. The Eccentric Connectivity Polynomial of some Graph Operations. Serdica Journal of Computing, Tome 5 (2011) no. 2, pp. 101-116. http://geodesic.mathdoc.fr/item/SJC_2011_5_2_a0/