Graph Operation Topological Index Eccentric Connectivity Polynomial
Issue Date:
2011
Publisher:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Journal of Computing, Vol. 5, No 2, (2011), 101p-116p
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.
