Eccentric connectivity index

By Aleksandar Ilić. 2011

120 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Physiology

View Paper: https://www.semanticscholar.org/paper/43f5cadedf457a8eae68aec1ea6cde8f712c44fd

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

  1. Modjtaba Ghorbani
  2. Mohammad Ali Hosseinzadeh
  3. Ivan Gutman
  4. A. c
  5. Bo Zhou
  6. Boris Furtula
  7. Ernesto Estrada
  8. Aleksandar Ilić

In Geometry and Topology

  1. Modjtaba Ghorbani
  2. Mohammad Ali Hosseinzadeh
  3. Ivan Gutman
  4. A. c
  5. Bo Zhou
  6. Aleksandar Ilić
  7. Boris Furtula
  8. Ernesto Estrada

In Physiology

  1. Ivan Gutman
  2. Modjtaba Ghorbani
  3. Mohammad Ali Hosseinzadeh
  4. A. c

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