# The Eccentric Connectivity Polynomial of some Graph Operations

• Volume: 5, Issue: 2, page 101-116
• ISSN: 1312-6555

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## Abstract

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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.* The work of this author was supported in part by a grant from IPM (No. 89050111).

## How to cite

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Ashrafi, A., Ghorbani, M., and Hossein-Zadeh, M.. "The Eccentric Connectivity Polynomial of some Graph Operations." Serdica Journal of Computing 5.2 (2011): 101-116. <http://eudml.org/doc/196270>.

@article{Ashrafi2011,
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).},
author = {Ashrafi, A., Ghorbani, M., Hossein-Zadeh, M.},
journal = {Serdica Journal of Computing},
keywords = {Graph Operation; Topological Index; Eccentric Connectivity Polynomial; graph operator; topological index; eccentric connectivity polynomial},
language = {eng},
number = {2},
pages = {101-116},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {The Eccentric Connectivity Polynomial of some Graph Operations},
url = {http://eudml.org/doc/196270},
volume = {5},
year = {2011},
}

TY - JOUR
AU - Ashrafi, A.
AU - Ghorbani, M.
TI - The Eccentric Connectivity Polynomial of some Graph Operations
JO - Serdica Journal of Computing
PY - 2011
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 5
IS - 2
SP - 101
EP - 116
AB - 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).
LA - eng
KW - Graph Operation; Topological Index; Eccentric Connectivity Polynomial; graph operator; topological index; eccentric connectivity polynomial
UR - http://eudml.org/doc/196270
ER -

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