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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 p<=n−1, we characterize those graphs which have the smallest eccentric connectivity index among all connected graphs of order n with p pendant vertices.
Field : Fen Bilimleri ve Matematik
Journal Type : Uluslararası
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