Admissible Property of Graphs in Terms of Independence Number

For a positive integer k , a graph G is said to have the property I k if each component of G has independence number at most k . The I 1 - admission number of a graph G , denoted by η ( G , I 1 ) , is the cardinality of a smallest vertex subset D such that V ( G ) = N G [ D ] or each component of G...

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Bibliographic Details
Published inBulletin of the Malaysian Mathematical Sciences Society Vol. 45; no. 5; pp. 2123 - 2135
Main Authors Hua, Hongbo, Hua, Xinying
Format Journal Article
LanguageEnglish
Published Singapore Springer Nature Singapore 01.09.2022
Springer Nature B.V
Subjects
Applications of Mathematics
Mathematics
Mathematics and Statistics
Bound
Admission number
Partial domination
Isolation number
Independence number
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Summary:For a positive integer k , a graph G is said to have the property I k if each component of G has independence number at most k . The I 1 - admission number of a graph G , denoted by η ( G , I 1 ) , is the cardinality of a smallest vertex subset D such that V ( G ) = N G [ D ] or each component of G - N G [ D ] is a clique. In this paper, we show that for a connected graph G of order n , if G ∉ { P 3 , C 6 } , then η ( G , I 1 ) ≤ 2 n 7 , and the bound is sharp.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-022-01335-8