Eccentric connectivity polynomial of some graph operations. (English) Zbl 1228.05180

Došlić, T.; Ghorbani, M.; Hosseinzadeh, M. A.

Util. Math. 84, 297-309 (2011).

Summary: The eccentricity connectivity polynomial of a graph \(G\) is defined as \[ \Xi(G;x)= \sum_{u\in V(G)} \delta_G(u) x^{\varepsilon_G(u)}, \] where \(\varepsilon_G(u)\) is the eccentricity of the vertex \(u\) and \(\delta_G(u)\) its degree. In this paper the eccentric connectivity polynomial is computed for several classes of composite graphs.

MSC:

05C31	Graph polynomials
05C40	Connectivity
05C90	Applications of graph theory

Keywords:

eccentric connectivity index; Cartesian product; graph operations; \(C_4\) nano tubes; \(C_4\) nano torus