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On the Paired-Domination Subdivision Number of a Graph

Author

Listed:
  • 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)

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 γ p r ( G ) of G . It is well known that sd γ p r ( G + e ) can be smaller or larger than sd γ 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 γ p r ( G + e ) ≤ sd γ p r ( G ) + 2 Δ ( G ) .

Suggested Citation

  • Guoliang Hao & Seyed Mahmoud Sheikholeslami & Mustapha Chellali & Rana Khoeilar & Hossein Karami, 2021. "On the Paired-Domination Subdivision Number of a Graph," Mathematics, MDPI, vol. 9(4), pages 1-9, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:439-:d:504284
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    References listed on IDEAS

    as
    1. J. Amjadi & R. Khoeilar & M. Chellali & Z. Shao, 2020. "On the Roman domination subdivision number of a graph," Journal of Combinatorial Optimization, Springer, vol. 40(2), pages 501-511, August.
    2. J. Amjadi & R. Khoeilar & M. Chellali & Z. Shao, 0. "On the Roman domination subdivision number of a graph," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-11.
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