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G-2018-69

Minimum eccentric connectivity index for graphs with fixed order and fixed number of pending vertices

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The eccentric connectivity index of a connected graph G is the sum over all vertices v of the product dG(v)eG(v), where dG(v) is the degree of v in G and eG(v) is the maximum distance between v and any other vertex of G. This index is helpful for the prediction of biological activities of diverse nature, a molecule being modeled as a graph where atoms are represented by vertices and chemical bonds by edges. We characterize those graphs which have the smallest eccentric connectivity index among all connected graphs of a given order n. Also, given two integers n and p with pn1, we characterize those graphs which have the smallest eccentric connectivity index among all connected graphs of order n with p pending vertices.

, 11 pages

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Yugoslav Journal of Operations Research, 29(2), 193–202, 2019 référence BibTeX