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• W1656845458 abstract "The eccentric connectivity index $xi^c$ is a novel distance--based molecular structure descriptor that was recently used for mathematical modeling of biological activities of diverse nature. It is defined as $xi^c (G) = sum_{v in V (G)} deg (v) cdot epsilon (v)$,, where $deg (v)$ and $epsilon (v)$ denote the vertex degree and eccentricity of $v$,, respectively. We survey some mathematical properties of this index and furthermore support the use of eccentric connectivity index as topological structure descriptor. We present the extremal trees and unicyclic graphs with maximum and minimum eccentric connectivity index subject to the certain graph constraints. Sharp lower and asymptotic upper bound for all graphs are given and various connections with other important graph invariants are established. In addition, we present explicit formulae for the values of eccentric connectivity index for several families of composite graphs and designed a linear algorithm for calculating the eccentric connectivity index of trees. Some open problems and related indices for further study are also listed." @default.
• W1656845458 created "2016-06-24" @default.
• W1656845458 creator A5024686169 @default.
• W1656845458 date "2011-03-13" @default.
• W1656845458 modified "2023-10-05" @default.
• W1656845458 title "Eccentric connectivity index" @default.
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• W1656845458 hasPublicationYear "2011" @default.
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