Inverse Co-even Domination of Graphs

Abstract

The purpose of this paper is to introduce a new inverse domination parameter in the graphs it is called inverse co-even domination number. Some properties of the theory to this definition were only touched. Also, many properties and limitations on this definition are determined. Additionally, some properties of inverse co-even domination number for some certain graphs and its complement are founded, such as regular, complete, path, cycle, wheel, complete bipartite, and star.

Bilangan Invers Dominasi Total Graf Helm Tertutup, Graf Gear, Graf Roda Ganda Dan Graf Antiweb-Gear

“…Penelitian mengenai bilangan dominasi, dominasi total dan bilangan invers dominasi total pada kelas-kelas graf tertentu telah menarik minat banyak peneliti (Dunbar et al, 1999;El-Zahar et al, 2008;Lan & Chang, 2013;Omran & Shalaan, 2020;Rusu & Spinrad, 2001). Terkait himpunan invers dominasi total, salah satu penerapannya yaitu pada jaringan komputer dengan kelompok komputer inti sebagai himpunan dominasi total dan kelompok komputer cadangan sebagai himpunan invers dominasi total (Kulli & Iyer, 2007).…”

Examining Captive and Inverse Captive Domination in Selected Graphs and Their Complements

“…The domination number 𝛾(𝐺) is the minimum cardinality of a dominating set D of G. If V-D contains a dominating set, then this set is called an inverse set of D in G. The symbol 𝛾 −1 (𝐺) represents the minimum cardinality over all inverse dominating set of G [2]. The concept of domination is used to solve many problems in various fields of mathematics subjects such as topological graphs [2,3], fuzzy graphs [4,5], and [6,7], number theory graph [8], general graphs [9][10][11][12][13][14][15][16][17][18], and others. The reader can be found all notions not mentioned [19][20][21][22].…”

Calculating Modern Roman Domination of Fan Graph and Double Fan Graph

“…In mathematics, this concept appeared in many fields including fuzzy graph [4][5][6] topological graph [7], polynomials domination [8,9], and others [10,11]. Additionally, many new definitions in this concept have been used, depending on putting some conditions on the dominating set [12], [13][14][15][16], out of dominating set [17][18][19] or on the two together as in [13]. A Roman dominating function on a graph 𝐺 = (𝑉; 𝐸) is a function 𝑓: 𝑉(𝐺) → {0,1,2}satisfying the condition that every vertex 𝑢 for which 𝑓(𝑢) = 0 is adjacent to at least one vertex 𝑣 for which 𝑓(𝑣) = 2, [20,21].…”