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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