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