Secure Fair Domination in Graphs

Author(s)	Ms. Apple Kate Aruyal Ambray, Prof. Dr. Enrico Enriquez, Prof. Dr. Grace Estrada, Prof. Dr. Edward Kiunisala
Country	Philippines
Abstract	Let G be a connected simple graph. A dominating set S⊆ V(G) is a fair dominating set in G if S=V(G) or if S≠V(G) and all vertices not in S are dominated by the same number of vertices from S, that is, \|N(u)∩ S\|=\|N(v)∩ S\|>0 for every two vertices u,v∈ V(G)∖S. A fair dominating set S of V(G) is a secure fair dominating set of G if for each u∈V(G)∖S, there exists v∈S such that uv∈E(G) and the set (S∖{v})∪ {u} is a fair dominating set of G. The minimum cardinality of a secure fair dominating set of G, denoted by γ_sfd (G), is called the secure fair domination number of G. In this paper, we initiate a study of secure fair domination in graphs and give some important results.
Keywords	dominating set, secure dominating set, fair dominating set, secure fair dominating set
Field	Mathematics
Published In	Volume 7, Issue 6, November-December 2025
Published On	2025-12-20
DOI	https://doi.org/10.36948/ijfmr.2025.v07i06.63971

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