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.