On the Paired-Domination Subdivision Number of a Graph

Guoliang Hao, Seyed Mahmoud Sheikholeslami, Mustapha Chellali, Rana Khoeilar and Hossein Karami
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Guoliang Hao: College of Science, East China University of Technology, Nanchang 330013, China
Seyed Mahmoud Sheikholeslami: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 51368, Iran
Mustapha Chellali: LAMDA-RO Laboratory, Department of Mathematics, University of Blida, B.P. 270, Blida 09000, Algeria
Rana Khoeilar: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 51368, Iran
Hossein Karami: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 51368, Iran

Mathematics, 2021, vol. 9, issue 4, 1-9

Abstract: In order to increase the paired-domination number of a graph G , the minimum number of edges that must be subdivided (where each edge in G can be subdivided no more than once) is called the paired-domination subdivision number sd ? p r ( G ) of G . It is well known that sd ? p r ( G + e ) can be smaller or larger than sd ? p r ( G ) for some edge e ? E ( G ) . In this note, we show that, if G is an isolated-free graph different from m K 2 , then, for every edge e ? E ( G ) , sd ? p r ( G + e ) ? sd ? p r ( G ) + 2 ? ( G ) .

Keywords: paired-domination number; paired-domination subdivision number (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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