Trees, unicyclic graphs extremal with respect to Kekule index
type: Item
instance of: scholarly article
zbMATH Open document ID: 1304.05019
author: A. Usha
author: P. S. Ranjini
author: V. Lokesha
publication date: 2014-10-15T00:00:00Z
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C07
Mathematics Subject Classification ID: 05C90
zbMATH DE Number: 6356041
zbMATH Keywords: tree
zbMATH Keywords: unicyclic graph
zbMATH Keywords: caterpillar
zbMATH Keywords: Kekule index
MaRDI profile type: Publication
title: Trees, unicyclic graphs extremal with respect to Kekule index
published in: Advanced Studies in Contemporary Mathematics (Kyungshang)
review text: The Kekule index of an undirected simple finite graph \(G\) is \(\sum_{\{u,v\}\in E(G)}|d(u)-d(v)|\) where \(d(u)\) is the degree of the vertex \(u\in V(G)\). The Kekule index belongs to a family of topological indices describing properties of graphs that are used for a characterization of chemical and biological activities of molecules modelled by the graph. Let \(\mathcal T_n\) be the family of all trees on an \(n\)-element set. It is proved that the path has the least Kekule index in \(\mathcal T_n\) and the star has the greatest Kekule index in \(\mathcal T_n\). The analogous result is obtained for unicyclic graphs (i.e. a cycle with pendent edges).
reviewed by: Václav Koubek
description: scientific article; zbMATH DE number 6356041