Inverse Frame Domination in Graphs

Abstract

The generalization of the concept of inverse frame domination on graphs is the fundamental point of this work. It has been shown to present modern properties on inverse frame domination and some corresponding theorems related to delete, add edges or remove vertices. The relationship between the initial graph and a graph obtaining from the edges of the contraction was also discussed.

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].…”