Fair Doubly Connected Domination in the Corona and the Cartesian Product of Two Graphs
Jan NiΓ±o C. Serrano - Β· International Journal of Mathematics Trends and Technology Β· 2023
Let πΊ be a nontrivial connected graph. A dominating set π β π(πΊ) is called a doubly connected dominating set of πΊ if both β¨πβ© and β¨π(πΊ)\πβ© are connected. If every distinct vertices π’ and v from π(πΊ)\π, |ππΊ (π’) β© π| = |ππΊ (π£) β© π|, then π is called a fair doubly connected dominating set of πΊ. Furthermore, the fair doubly connected domination number, denoted by Ξ³πππ(πΊ), is the minimum cardinality of a fair doubly connected dominating set of G. A fair doubly connected dominating set of cardinality πΎπππ(πΊ) is called πΎπππ-set. In this paper, we characterized the fair doubly connected domination in the corona and Cartesian product of two graphs and give some important results