\(L(2,1)\)-labeling for subdivisions of cycle dominated graphs
type: Item
instance of: scholarly article
title: \(L(2,1)\)-labeling for subdivisions of cycle dominated graphs
zbMATH Open document ID: 1393.05233
author: Muthali Murugan
published in: Bulletin of Computational Applied Mathematics
publication date: 2018-08-07T00:00:00Z
full work available at URL: http://drive.google.com/open
review text: Summary: Let \(G(V,E)\) be a simple, finite, connected, undirected graph. Distance two labeling or \(L(2,1)\)-labeling of a graph \(G\) is an assignment \(f\) from the vertex set \(V(G)\) to the set of non-negative integers such that \(| f(x)-f(y)| \geq 2\) if \(x\) and \(y\) are adjacent and \(| f(x)-f(y)| \geq 1\) if \(x\) and \(y\) are at distance 2, for all \(x\) and \(y\) in \(V(G)\). The \(L(2,1)\)-labeling number \(\lambda(G)\) of \(G\) is the smallest number \(k\) such that \(G\) has an \(L(2,1)\)-labeling \(f\) with \(\max\{f(v):v\in V(G)\}=k\). In this paper, we construct \(L(2,1)\)-labeling of subdivisions of cycle dominated graphs like subdivided Double Fans, subdivided \(nC_\alpha\) with a common vertex and subdivided Books \(B_n\) and hence we find the \(\lambda\)-number of these graphs.
Mathematics Subject Classification ID: 05C78
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 05C12
zbMATH DE Number: 6914247
zbMATH Keywords: distance two labeling
zbMATH Keywords: transmitters
zbMATH Keywords: channel assignment
zbMATH Keywords: double fan
MaRDI profile type: Publication
cites work: Q5422499
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description: scientific article; zbMATH DE number 6914247