Pitchfork Edge Domination in Graphs
Asia Pacific Journal of Mathematics · 2024
This study presents the pitchfork edge domination, a novel model of domination in graphs is introduced here.Let G = (V, E) be a simple, finite and undirected graph without isolated edges.A set of edges De is said to be pitchfork edge dominating set if r ≤ |N (e) (E -De)| ≤ s for every e ∈ De, where r and s are non-negative integers.That means every edge e ∈ De dominates at least r and at most s edges of E -De.The minimum cardinality for all pitchfork edge dominating sets in G is the pitchfork edge domination number γ pf e (G).Pitchfork edge domination at r = 1 and s = 2 is discussed in this paper.There are certain limitations on γ pf e (G) pertaining to the order, size, minimum degree and maximum degree of the graph and other properties are proved here.Pitchfork edge domination is applied for some well-known graphs.