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New parameter of inverse domination in graphs

Author

Listed:
  • Mohammed A. Abdlhusein

    (University of Baghdad
    University of Thi-Qar)

  • Manal N. Al-Harere

    (University of Technology)

Abstract

Let G be a finite graph, simple, undirected and has no isolated vertex. A dominating set D of G is said a pitchfork dominating set (pds) if every v in it dominates at most k and at least j vertices out of D, for any non-negative integers j and k. The pitchfork domination number (pdn) of G, denoted by $$\gamma _{pf}(G)$$ γ pf ( G ) is the order of a minimum pds in G. In this paper, the inverse pitchfork domination is introduced, the definition is used for $$j=1$$ j = 1 and $$k=2$$ k = 2 . Several bounds are determined that are associated with size, order, maximum degree and minimum degree of a graph. Also, this type of domination on some known graphs is calculated, like: path, cycle, complete, complete bipartite and wheel graph. The essential conditions for any graph having an inverse pitchfork domination are discussed.

Suggested Citation

  • Mohammed A. Abdlhusein & Manal N. Al-Harere, 2021. "New parameter of inverse domination in graphs," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(1), pages 281-288, March.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:1:d:10.1007_s13226-021-00082-z
    DOI: 10.1007/s13226-021-00082-z
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