2-Domination in vague graphs

Document Type : Research Paper

Authors

1 Department of Knowledge and Cognitive Intelligence, Imam Hossein University, Tehran, Iran.

2 Department of Mathematics, Shahid Beheshti University, Tehran, Iran.

3 Department of Mathematics, Faculty of Science, Payam Noor University, Tehran, Iran.

10.29252/as.2021.2164

Abstract

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.

Keywords


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