A Note on the Paired-Domination Subdivision Number of Trees

Xiaoli Qiang, Saeed Kosari, Zehui Shao, Seyed Mahmoud Sheikholeslami, Mustapha Chellali and Hossein Karami
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Xiaoli Qiang: Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
Saeed Kosari: Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
Zehui Shao: Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, 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, Algeria
Hossein Karami: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 51368, Iran

Mathematics, 2021, vol. 9, issue 2, 1-9

Abstract: For a graph G with no isolated vertex, let γ p r ( G ) and sd γ p r ( G ) denote the paired-domination and paired-domination subdivision numbers, respectively. In this note, we show that if T is a tree of order n ≥ 4 different from a healthy spider (subdivided star), then sd γ p r ( T ) ≤ min { γ p r ( T ) 2 + 1 , n 2 } , improving the ( n − 1 ) -upper bound that was recently proven.

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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