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 total irregularity of a graph G is defined as 〖irr〗_t (G)=1/2 ∑_(u,v∈V(G))▒〖|d_u-d_v |〗, where d_u denotes the degree of a vertex u∈V(G). In this paper by using the Gini index, we obtain the ordering of the total irregularity index for some classes of connected graphs, with the same number of vertices.

The irregularity of a simple undirected graph G was defined by Albertson [5] as irr(G) = ∑ uv∈E(G) |dG(u)− dG(v)|, where dG(u) denotes the degree of a vertex u ∈ V (G). In this paper we consider the irregularity of graphs under several graph operations including join, Cartesian product, direct product, strong product, corona product, lexicographic product, disjunction and symmetric difference. ...

INTRODUCTION There is no consensus on the length of ECG tracing that should be recorded to represent adequate rate control in patients with atrial fibrillation (AFib). The purpose of the study was to examine whether heart rate measurements based on short-term ECGs recorded at different periods of the day may correspond to the mean heart rate and rate irregularity analyzed from standard 24-hour ...

An assignment of positive integer weights to the edges of a simple graph G is called irregular, if the weighted degrees of the vertices are all different. The irregularity strength, s(G), is the maximal weight, minimized over all irregular assignments. In this study, we show that s(G) c1 n / , for graphs with maximum degree n and minimum

One of the important clinical features that differentiates benign melanocytic nevi from malignant melanomas is the irregularity of the lesion border. There are two types of border irregularities: texture irregularities, the small variations along the border, and structure irregularities, the global indentations and protrusions. Texture irregularities are subject to noise, whereas structure irre...

Martin Bača et al. [2] introduced the problem of determining the total vertex irregularity strengths of graphs. In this paper we discuss how the addition of new edge affect the total vertex irregularity strength.