On \(\text{Ł}(\wp, \wp - 1, \dots, 1)\) labelings of circulant graphs
type: Item
instance of: scholarly article
title: On \(\text{Ł}(\wp, \wp - 1, \dots, 1)\) labelings of circulant graphs
zbMATH Open document ID: 1477.05162
DOI: 10.1155/2021/6578478
author: K. Mageshwaran
author: Ali Ahmad
author: Bundit Unyong
author: G. Kalaimurugan
author: S. Gopinath
published in: Journal of Mathematics
publication date: 2021-11-24T00:00:00Z
review text: Summary: An \(m\)-\(\text{Ł}(\wp, \wp - 1, \dots, 1)\) labeling of a simple graph \(\mathscr{G}\) is a mapping \(\tau\) from the vertex set \(\vee(\mathscr{G})\) to \(\{0, 1, \dots, m\}\) such that \(|\tau(u) - \tau(v)|\geq\wp+1-\mathfrak{d}(u, v)\), \(\forall u,v\in\vee(\mathscr{G})\), where length of the shortest route connecting \(u\) and \(v\) is represented by \(\mathfrak{d}(u, v)\). The smallest \(m\) for which there exists a \(m\)-\(\text{Ł}(\wp, \wp - 1, \dots, 1)\) labeling of \(\mathscr{G}\) is known as the \(\text{Ł}(\wp,\wp - 1, \dots, 1)\) labeling number of \(\mathscr{G}\), and it is described by \(\lambda_\wp(\mathscr{G})\). We define \(m\)-\(\text{Ł}^\prime(\wp,\wp - 1, \dots, 1)\) as the same as the \(m\)-\(\text{Ł}(\wp, \wp - 1, \dots, 1)\) labeling if \(\tau\) is one to one. The \(\text{Ł}^\prime(\wp, \wp - 1, \dots, 1)\) labeling number of \(\mathscr{G}\) represented by \(\lambda(\wp, \wp - 1, \dots, 1)_\prime( \mathscr{G})\) and is called minimum span. In this paper, we prove that the circulant graphs with specified generating sets admit \(m\)-\(\text{Ł}(\wp, \wp - 1, \dots, 1)\) and \(m\)-\(\text{Ł}^\prime(\wp, \wp - 1, \dots, 1)\) labeling and also find \(\lambda_\wp(\mathscr{G})\) and \(\lambda (\wp ,\wp - 1, \dots, 1)^\prime(\mathscr{G})\). Moreover, we find the \(\text{Ł}(\wp, \wp - 1, \dots, 1)\) labeling number of any simple graph with diameter less than \(\wp\).
Mathematics Subject Classification ID: 05C78
zbMATH DE Number: 7433088
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/6578478
OpenAlex ID: W3205767669
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description: scientific article; zbMATH DE number 7433088