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A new method for computing the eccentric connectivity index of fullerenes. (English) Zbl 1293.05189

Summary: The eccentric connectivity index of the molecular graph \(G\), \(\xi^c (G)\), was proposed by V. Sharma, R. Goswami and A. K. Madan [J. Chem. Inf. Comput. Sci., 37, No. 2, 273–282 (1997; doi:10.1021/ci960049h)]. It is defined as \(\xi^c (G) = \sum_{u\in V(G)}\operatorname{deg}G(u) \operatorname{ecc}(u)\), where \(\operatorname{deg}G(x)\) denotes the degree of the vertex \(x\) in \(G\) and \(\mathrm{ecc}(u) = \max\{d(x, u) \mid x\in V (G)\}\). In this paper this graph invariant is computed for an infinite class of fullerenes by means of group action.

MSC:

05C40 Connectivity
05C90 Applications of graph theory
05C12 Distance in graphs
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