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Open AccessArticle

A Note on the Paired-Domination Subdivision Number of Trees

1
Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
2
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 51368, Iran
3
LAMDA-RO Laboratory, Department of Mathematics, University of Blida, B.P. 270 Blida, Algeria
*
Author to whom correspondence should be addressed.
Mathematics 2021, 9(2), 181; https://doi.org/10.3390/math9020181
Received: 13 December 2020 / Revised: 10 January 2021 / Accepted: 15 January 2021 / Published: 18 January 2021
(This article belongs to the Special Issue Graphs, Metrics and Models)
For a graph G with no isolated vertex, let γpr(G) and sdγpr(G) denote the paired-domination and paired-domination subdivision numbers, respectively. In this note, we show that if T is a tree of order n4 different from a healthy spider (subdivided star), then sdγpr(T)min{γpr(T)2+1,n2}, improving the (n1)-upper bound that was recently proven. View Full-Text
Keywords: paired-domination number; paired-domination subdivision number paired-domination number; paired-domination subdivision number
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MDPI and ACS Style

Qiang, X.; Kosari, S.; Shao, Z.; Sheikholeslami, S.M.; Chellali, M.; Karami, H. A Note on the Paired-Domination Subdivision Number of Trees. Mathematics 2021, 9, 181. https://doi.org/10.3390/math9020181

AMA Style

Qiang X, Kosari S, Shao Z, Sheikholeslami SM, Chellali M, Karami H. A Note on the Paired-Domination Subdivision Number of Trees. Mathematics. 2021; 9(2):181. https://doi.org/10.3390/math9020181

Chicago/Turabian Style

Qiang, Xiaoli; Kosari, Saeed; Shao, Zehui; Sheikholeslami, Seyed M.; Chellali, Mustapha; Karami, Hossein. 2021. "A Note on the Paired-Domination Subdivision Number of Trees" Mathematics 9, no. 2: 181. https://doi.org/10.3390/math9020181

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