International Journal of Nonlinear Analysis and Applications

Stability of (1,2)-total pitchfork domination

Document Type : Research Paper

Authors

Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq

Abstract

Let G=(V,E) be a finite, simple, and undirected graph without an isolated vertex. We define a dominating  D of V(G) as a total pitchfork dominating set if 1≤|N(t)∩V−D|≤2 for every t∈D such that G[D] has no isolated vertex. In this paper, the effects of adding or removing an edge and removing a vertex from a graph are studied on the order of minimum total pitchfork dominating set γpft(G) and the order of minimum inverse total pitchfork dominating set γpf−t(G). Where γpft(G) is proved here to be increasing by adding an edge and decreasing by removing an edge, which are impossible cases in the ordinary total domination number.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 4
April 2025
Pages 233-240
  • Receive Date: 24 February 2021
  • Accept Date: 25 April 2021