New parameter of inverse domination in graphs

Mohammed A. Abdlhusein () and Manal N. Al-Harere ()
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Mohammed A. Abdlhusein: University of Baghdad
Manal N. Al-Harere: University of Technology

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 1, 281-288

Abstract: 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.

Keywords: Pitchfork domination; Inverse pitchfork domination; Path; Cycle; Bipartite graph; 05C69 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00082-z

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