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A Note on the Paired-Domination Subdivision Number of Trees

Author

Listed:
  • 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)

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.

Suggested Citation

  • Xiaoli Qiang & Saeed Kosari & Zehui Shao & Seyed Mahmoud Sheikholeslami & Mustapha Chellali & Hossein Karami, 2021. "A Note on the Paired-Domination Subdivision Number of Trees," Mathematics, MDPI, vol. 9(2), pages 1-9, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:181-:d:482140
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