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On the Paired-Domination Subdivision Number of Trees

Author

Listed:
  • 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)

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 γ pr ( G ) of G . The paired-domination subdivision number sd γ 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 γ pr ( T ) + sd γ pr ( T + e ) ≤ n + 2.

Suggested Citation

  • Shouliu Wei & Guoliang Hao & Seyed Mahmoud Sheikholeslami & Rana Khoeilar & Hossein Karami, 2021. "On the Paired-Domination Subdivision Number of Trees," Mathematics, MDPI, vol. 9(10), pages 1-10, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1135-:d:556260
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