۲-Domination in vague graphs

A vague graph is a generalized 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. In this paper, the notions of (perfect-total) ۲-dominating set and (perfect-total) ۲-domination numbers on vague graphs are introduced and some properties are investigated. Especially, it is proven that in any strong vague graph on a Petersen graph, any minimal ۲-dominating set is a minimal perfect ۲-dominating set and minimal dominating set. Then, the concepts of (total) ۲-cobondage set and (total) ۲-cobondage number in vague graphs are expressed and related results obtained. Finally, an application related to Fire Stations and Emergency Medical centers is provided.

کلیدواژه ها:

Vague graph ، ۲-dominating set ، ۲-cobondage set