An edge irregular total k-labeling of a graph G is a labeling of the vertices and edges with labels 1, 2, . . . , k such that the weights of any two different edges are distinct, where the weight of an edge is the sum of the label of the edge itself and the labels of its two end vertices. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregul...

An edge irregular total k-labeling of a graph G = (V,E) is a labeling φ : V ∪ E → {1, 2, . . . , k} such that the total edge-weights wt(xy) = φ(x) + φ(xy) + φ(y) are different for all pairs of distinct edges. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength of G. In this paper, we determined the exact values of the total e...

An edge irregular total k-labeling φ : V (G)∪E(G) → {1, 2, . . . , k} of a graph G = (V,E) is a labeling of vertices and edges of G in such a way that for any different edges xy and x′y′ their weights φ(x) + φ(xy) + φ(y) and φ(x′) + φ(x′y′) + φ(y′) are distinct. The total edge irregularity strength, tes(G), is defined as the minimum k for which G has an edge irregular total k-labeling. We have ...

Let G be a simple graph of n order. An edge labeling such that the weights all vertex are different and elements set modulo n, called modular irregular labeling. The irregularity strength is minimum positive integer k have If none, then we infinity. In this article, determine complete graphs.

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...