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.

Track Irregularity has a significant influence on the safety of train operation. Due to the fact that the extremely large number of factors affect track irregularity, it is challenging to find a concise yet effective mathematical method to describe the evolution of track irregularity. In this paper, inspection data generated by GJ-4 track inspection cars from Jinan Railway Bureau in China were ...

OBJECTIVE To evaluate mandibular irregularity index stability following orthodontic treatment facilitated by alveolar corticotomy and augmentation bone grafting (Cort+). MATERIALS AND METHODS The irregularity index of 121 orthodontically treated and 15 untreated patient study casts was analyzed at 5 years and 10 years. RESULTS Cort+ resulted in significantly lower mandibular irregularity in...

The propagation of shear waves differs between geo-media due to layer’s structure and irregularity present in different layers. This paper studies the propagation of shear waves in a monoclinic layer with irregularity lying between two isotropic semiinfinite elastic medium. The displacement in the monoclinic layer is obtained by using perturbation technique. Then the dispersion relation is foun...

Albertson [3] has defined the irregularity of a simple undirected graph G = (V,E) as irr(G) = ∑ uv∈E |dG(u)− dG(v)| , where dG(u) denotes the degree of a vertex u ∈ V . Recently, this graph invariant gained interest in the chemical graph theory, where it occured in some bounds on the first and the second Zagreb index, and was named the third Zagreb index [13]. For general graphs with n vertices...

Railway track irregularity surveying is important for the construction and the maintenance of railway lines. With the development of inertial devices, systems based on Inertial Navigation System (INS) have become feasible and popular approaches in track surveying applications. In order to overcome the requirement of high precision control points, this paper proposes a railway track irregularity...

Measures of the irregularity of chemical graphs could be helpful for QSAR/QSPR studies and for the descriptive purposes of biological and chemical properties, such as melting and boiling points, toxicity and resistance. Here we consider the following four established irregularity measures: the irregularity index by Albertson, the total irregularity, the variance of vertex degrees and the Collat...

• The design method based on Voronoi was proposed to mimic the characteristics of cancellous bone in human body. Ceramic Digital light processing (DLP) adopted satisfy forming requirements irregular scaffolds. compressive strength scaffolds can be increased by 30% through regulation irregularity. Cell experiments confirmed that structural changes also had influence biocompatibility Ideal requir...

The irregularity of a graph G is defined as the sum of weights |d(u) − d(v)| of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G, respectively. In this paper, some structural properties on trees with maximum (or minimum) irregularity among trees with given degree sequence and trees with given branching number are explored, respectively. Moreover, the correspon...

The propagation of shear waves in an anisotropic fluid saturated porous layer over a prestressed semi-infinite homogeneous elastic half-space lying under an elastic homogeneous layer with irregularity present at the interface with rigid boundary has been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for shear waves is derived by using the pertur...