Title: |
Secure Fair Domination in the Join of Two Graphs |
Authors: |
Apple Kate A. Ambray, Enrico L. Enriquez |
Source: |
International Journal of Latest Engineering Research and Applications, pp 01 - 09, Vol 11 - No. 01, 2026 |
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 γsfd(G), is called the secure fair domination number of G. In this paper, we give some results on the secure fair domination in the join of two nontrivial connected graphs. |
Kaywords: |
Keywords: dominating set, secure dominating set, fair dominating set, secure fair dominating set, join of two graphs |
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DOI: |
10.56581/IJLERA.11.01.01-09 |
