%0 Journal Article %T 2-Domination in vague graphs %J Algebraic Structures and Their Applications %I Yazd University %Z 2382-9761 %A Banitalebi, Sadegh %A Borzooei, Rajab Ali %A Mohamadzadeh, Elahe %D 2021 %\ 08/01/2021 %V 8 %N 2 %P 203-222 %! 2-Domination in vague graphs %K Vague graph %K 2-dominating set %K 2-cobondage set %R 10.22034/as.2021.2164 %X 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) 2-dominating set and (perfect-total) 2-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 2-dominating set is a minimal perfect 2-dominating set and minimal dominating set. Then, the concepts of (total) 2-cobondage set and (total) 2-cobondage number in vague graphs are expressed and related results obtained. Finally, an application related to Fire Stations and Emergency Medical centers is provided. %U https://as.yazd.ac.ir/article_2164_344def5b5d8b2e369fe87ce289c94d72.pdf