Equitable Domination in Neutrosophic Graph Using Strong Arc

Abstract

In this paper, we have initiated the study of domination and equitable domination of Neutrosophic graphs using strong arcs. Strong arcs represent the optimal (minimum) degree of truth membership value, the optimal (minimum) degree of indeterminacy membership value, and the non-optimal ( maximum) degree of falsity membership value. Hence, the studies of domination and equitable domination using strong arcs have been explored. Upper bounds and minimality conditions for the existence of the introduced parameters were discussed. Extend the studies on strong and weak equitable domination of Neutrosophic graphs and obtain the relationship between domination and the equitable domination parameter. Furthermore, we have provided some theorems based on equitable domination of Neutrosophic graphs and discussed the upper and lower bounds of the strong and weak equitable domination in terms of order and size with other existing domination parameters of Neutrosophic graphs.

Keywords

• domination
• equitable domination
• strong arc