The Eccentric Connectivity Polynomial of some Graph Operations
The Eccentric Connectivity Polynomial of some Graph Operations
复制标题
DOI：
10.55630/sjc.2011.5.101-116
复制
发表时间：
2011-07
期刊：
影响因子：
--
通讯作者：
A. Ashrafi;M. Ghorbani;M. Hosseinzadeh
中科院分区：
文献类型：
--
作者：
A. Ashrafi;M. Ghorbani;M. Hosseinzadeh
图G的偏心连通度指数是由Sharma，Goswami和Madan提出的。定义它为：∑ ^C（G）= ∑ u ∈ V（G）degG（u）εG（u），其中degG（u）表示G中顶点x的度，εG（u）= Max{d（u，x）|x ∈ V（G）}.偏心连通多项式是该拓扑指数的多项式形式。本文给出了图的笛卡尔积、对称差、析取和并的偏心连通多项式的精确公式。
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.