On the Wiener Complexity and the Wiener Index of Fullerene Graphs

Andrey A. Dobrynin and Andrei Yu Vesnin
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Andrey A. Dobrynin: Laboratory of Topology and Dynamics, Novosibirsk State University, 630090 Novosibirsk, Russia
Andrei Yu Vesnin: Laboratory of Topology and Dynamics, Novosibirsk State University, 630090 Novosibirsk, Russia

Mathematics, 2019, vol. 7, issue 11, 1-17

Abstract: Fullerenes are molecules that can be presented in the form of cage-like polyhedra, consisting only of carbon atoms. Fullerene graphs are mathematical models of fullerene molecules. The transmission of a vertex v of a graph is a local graph invariant defined as the sum of distances from v to all the other vertices. The number of different vertex transmissions is called the Wiener complexity of a graph. Some calculation results on the Wiener complexity and the Wiener index of fullerene graphs of order n ≤ 232 and IPR fullerene graphs of order n ≤ 270 are presented. The structure of graphs with the maximal Wiener complexity or the maximal Wiener index is discussed, and formulas for the Wiener index of several families of graphs are obtained.

Keywords: graph; fullerene; Wiener index; Wiener complexity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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