Admissible property of graphs in terms of independence number
type: Item
instance of: scholarly article
title: Admissible property of graphs in terms of independence number
zbMATH Open document ID: 1500.05049
author: Xinying Hua
author: Hongbo Hua
published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series
publication date: 2022-10-04T00:00:00Z
review text: For a graph \(G\) and a property \(\mathcal{P}\), a subset \(D\subseteq V(G)\) is said to be a \(\mathcal{P}\)-admissible set of \(G\) if \(G-N_{G}[D]\) admits the property \(\mathcal{P}\), where \(N_{G}[D]= D\cup N_{G}(D)\). The \(\mathcal{P}\)-admission number of \(G\) is the cardinality of a minimum \(\mathcal{P}\)-admissible set in \(G\). A graph \(G\) is said to have the property \(\mathcal{I}_{k}\) if the independence number of each component of \(G\) is at most \(k\). As a generalization of the domination number and isolation number, the \(\mathcal{P}\)-admission number was proposed and investigated by \textit{H. Yu} and \textit{B. Wu} [Graphs Comb. 38, No. 1, Paper No. 6, 9 p. (2022; Zbl 1479.05290)]. In this paper, the authors establish a sharp upper bound for \(\mathcal{I}_{1}\)-admission number of generally connected graphs.
reviewed by: Baoyindureng Wu
Mathematics Subject Classification ID: 05C69
zbMATH DE Number: 7596038
zbMATH Keywords: partial domination
zbMATH Keywords: isolation number
zbMATH Keywords: independence number
zbMATH Keywords: \({\mathcal{I}}_1 \)-admission number
zbMATH Keywords: bound
MaRDI profile type: Publication
full work available at URL: s40840-022-01335-8
OpenAlex ID: W4283120775
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DOI: 10.1007/S40840-022-01335-8
description: scientific article; zbMATH DE number 7596038