New concepts of domination sets in vague graphs with applications

A vague graph is a generalised structure of a fuzzy graph that gives more precision, flexibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs, which is introduced by Ramakrishna (2009). Domination in graphs has many applications to several fields. Domination arises in facility location problems, where the number of facilities (e.g., hospitals, fire stations) is fixed and one attempts to minimise the distance that a person needs to travel to get to the closest facility. Concepts from domination set also appear in problems involving finding sets of representatives in monitoring communication or electrical networks, and in land surveyor must stand in order to take height measurements for an entire region. Hence, in this paper, double domination of vague graphs is introduced and some basic theorems are proved. An interesting result on γdd(G) using some known parameter of G is obtained. Finally, some applications of domination in vague graph are given.