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.

Abstract Consider the complete graph on n vertices. To each vertex assign an Ising spin that can take values $$-1$$ - 1 or $$+1$$ + . Each $$i \in [n]=\{1,2,\dots , n\}$$ i ∈ [ n <mml:m...

There are two key characteristic of animal and human societies: (1) degree heterogeneity, meaning that not all individual have the same number of associates; and (2) the interaction topology is not static, i.e. either individuals interact with different set of individuals at different times of their life, or at least they have different associations than their parents. Earlier works have shown ...

Let G(V;E) be a graph. The common neighborhood graph (congraph) of G is a graph with vertex set V , in which two vertices are adjacent if and only if they have a common neighbor in G. In this paper, we obtain characteristics of congraphs under graph operations; Graph :::::union:::::, Graph cartesian product, Graph tensor product, and Graph join, and relations between Cayley graphs and its c...

of the Dissertation Theshold Dynamics for Statistical Density Estimation and Graph Clustering

In this paper, dynamics of the well-known differential gear train mechanism is presented in a systematic manner using the unified approach of bond graph. The approach offers an alternative to the conventional energy based methods. The dynamics of the mechanism is also quite significant from the point of view of design. Reaction forces and moments at different locations, which are of interest fr...

In this paper, we propose a distributed continuoustime linear dynamics for solving the localization problem based on signal angle-of-arrival information. We first formulate the AOA localization problem within the framework of formation graph theory, which is an extension of the classical graph theory by incorporating the positional information of the vertices. Solving the AOA localization probl...