Some results on harmonic mean graphs
type: Item
instance of: scholarly article
zbMATH Open document ID: 1251.05128
publication date: 2012-09-11T00:00:00Z
full work available at URL: index.html
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 05C78
zbMATH DE Number: 6080562
zbMATH Keywords: graph
zbMATH Keywords: harmonic mean graph
zbMATH Keywords: crown
zbMATH Keywords: wheel
zbMATH Keywords: prism
MaRDI profile type: Publication
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author: S. S. Sandhya
author: S. Somasundaram
author: R. Ponraj
title: Some results on harmonic mean graphs
published in: International Journal of Contemporary Mathematical Sciences
review text: A graph \(G\) is called a Harmonic mean graph if it is possible to label its vertices with distinct labels \(f(x)\in\{1,2,\dots,|E(G)|+1\}\) in such a way that when each edge \(e=uv\) is labelled with NEWLINE\[NEWLINEf(uv)=\left\lceil\frac{2f(u)f(v)}{f(u)+f(v)}\right\rceil \text{or} \left\lfloor\frac{2f(u)f(v)}{f(u)+f(v)}\right\rfloorNEWLINE\]NEWLINE then the edge labels are distinct.NEWLINENEWLINEThe main contribution of the paper is a constructive proof that selected classes of graphs, namely \(C_m\cup P_n\), \(m\geq 3\), \(n>1\), \(C_m \cup C_n\), \(m\geq 3\), \(n\geq3\), \(nK_3\), \(nK_3 \cup P_m\), \(m>1\), \(mC_4\), \(mC_4\cup P_n\), \(nK_3\cup mC_4\) and crown are harmonic mean graphs.
reviewed by: Vladimír Lacko
description: scientific article; zbMATH DE number 6080562