in this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. also, density and balanced irregular vague graphs are discussed and some of their properties are established. finally we give an application of vague digraphs.

In this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. Also, density and balanced irregular vague graphs are discussed and some of their properties are established. Finally we give an application of vague digraphs.

The concept of vague graph was introduced by Ramakrishna in [12]. 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. The main purpose of this paper is to introduce the concept of dominating set, perfect dominating set, minimal perfect dominating set and i...

The hesitant fuzzy graph (HFG) is one of the most powerful tools to find strongest influential person in a network. Many problems practical interest can be modeled and solved by using HFG algorithms. HFGs, belonging FG family, have good capabilities when faced with that cannot expressed FGs. vague-valued (VVHFG) generalization HFG. A VVHFG useful tool various parts, such as meetings, conference...

in this paper, various elementary properties of vague rings are obtained. furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

Vague graphs (VGs), belonging to the fuzzy (FGs) family, have good capabilities when faced with problems that cannot be expressed by FGs. The notion of a VG is new mathematical attitude model ambiguity and uncertainty in decision-making issues. A vague graph structure (VFGS) generalization VG. It powerful useful tool find influential person various relations. VFGSs can deal associated inconsist...