On the Paired-Domination Subdivision Number of Trees

Shouliu Wei, Guoliang Hao, Seyed Mahmoud Sheikholeslami, Rana Khoeilar and Hossein Karami
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Shouliu Wei: College of Mathematics and Data Science, Minjiang University, Fuzhou 350108, China
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
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 10, 1-10

Abstract: A paired-dominating set of a graph G without isolated vertices is a dominating set of vertices whose induced subgraph has perfect matching. The minimum cardinality of a paired-dominating set of G is called the paired-domination number ? pr ( G ) of G . The paired-domination subdivision number sd ? pr ( G ) of G is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the paired-domination number. Here, we show that, for each tree T ? P 5 of order n ? 3 and each edge e ? E ( T ), sd ? pr ( T ) + sd ? pr ( T + e ) ? n + 2.

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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