Bounds on co-independent liar's domination in graphs
type: Item
instance of: scholarly article
title: Bounds on co-independent liar's domination in graphs
zbMATH Open document ID: 1477.05138
DOI: 10.1155/2021/5544559
author: K. Suriya Prabha
author: S. Amutha
author: N. Anbazhagan
author: Ismail Naci Cangül
published in: Journal of Mathematics
publication date: 2021-06-22T00:00:00Z
review text: Summary: A set \(S\subseteq V\) of a graph \(G=(V,E)\) is called a co-independent liar's dominating set of \(G\) if (i) for all \(v\in V\), \(|N_G [v] \cap S|\geq 2\), (ii) for every pair \(u\), \(v\in V\) of distinct vertices, \(|(N_G [u] \cup N_G [v]) \cap S|\geq 3\), and (iii) the induced subgraph of \(G\) on \(V-S\) has no edge. The minimum cardinality of vertices in such a set is called the co-independent liar's domination number of \(G\), and it is denoted by \(\gamma_{\text{coi}}^{LR} (G)\). In this paper, we introduce the concept of co-independent liar's domination number of the middle graph of some standard graphs such as path and cycle graphs, and we propose some bounds on this new parameter.
Mathematics Subject Classification ID: 05C69
zbMATH DE Number: 7361849
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/5544559
OpenAlex ID: W3138990490
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description: scientific article; zbMATH DE number 7361849