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Total eccentricity index of the generalized hierarchical product of graphs. (English) Zbl 1392.05059
Summary: Let \(G=(V(G),E(G))\) be a connected graph. The total eccentricity index of \(G\) is defined as \(\zeta (G)=\sum \nolimits _{v\in V(G)}{{{\varepsilon }_{G}}(v)}\), where \({{\varepsilon }_{G}}(v)\) is the eccentricity of the vertex \(v\). In this paper, we compute the total eccentricity of generalized hierarchical product of graphs. Moreover, we derive some explicit formulae for total eccentricity index of F-sum graph, Cartesian product, Cluster product and Corona product of graphs and apply those results to find the total eccentricity index of various classes of chemical graphs and nanostructures.

MSC:
05C35 Extremal problems in graph theory
05C07 Vertex degrees
05C40 Connectivity
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