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Certain Notions of Regularity in Vague Graphs with Novel Application
Zehui Shao, Yongsheng Rao, Saeed Kosari, Hossein Rashmanlou and F. Mofidnakhaei

Vague set as a generalization of fuzzy set increase its elasticity drastically. Vague graph is an extended structure of a fuzzy graph which gives more precision, flexibility, and compatibility to the system when compared with the classical, fuzzy and vague models. In this paper we first introduce the notion of perfectly regular vague graph that is both regular and totally regular. Then we present the concepts of strongly edge irregular vague graphs and strongly edge totally irregular vague graphs. A comparative study between strongly edge irregular vague graphs and strongly edge totally irregular vague graphs is done. Finally we give an application of vague digraph in travel time.

Keywords: Vague set, vague graphs, edge irregular, perfectly regular, total degree

Mathematics Subject Classification: 05C99, 03E72

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