On edge irregularity strength of graphs

An edge irregular total k-labeling ϕ :

Indonesian Journal of Combinatorics, 2021

An edge irregular total k-labeling f : V ∪ E → {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 two different edges uv and u v , their weights f (u) + f (uv) + f (v) and f (u) + f (u v) + f (v) are distinct.The total edge irregularity strength tes(G) is defined as the minimum k for which the graph G has an edge irregular total k-labeling. In this paper, we determine the total edge irregularity strength of new classes of graphs C m @C n , P * m,n and C * m,n and hence we extend the validity of the conjecture tes(G) = max |E(G)|+2 3 , ∆(G)+1 2 for some more graphs.

Palestine Journal of Mathematics , 2018

Abstract. A vertex irregular total k-labeling of a graph G with vertex setV and edge set E is an assignment of positive integer labels {1,2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of G, denoted bytvs(G) is the minimum value of the largest label k over all such irregular assignment. In this paper, we study the total vertex irregularity strength of cycle quadrilateral snake, s unflower, double wheel, fungus, triangular book and quadrilateral book.

A totally irregular total k-labeling

Let G be a connected graph with a non empty vertex set V (G) and edge set E(G). An edge irregular total k-labeling of a graph G is a labeling λ : V (G) ∪ E(G) → {1, 2, ..., k}, so that every two different edges have different weights. The weight of edge uv of G is the sum of the labels vertices u and v and label of the edge uv, which is can be written as wt(uv) = λ(u) + λ(uv) + λ(v). The total edge irregularity strength of G, denoted by tes(G) is the minimum positive integer k for which the graph G has an edge irregular total k-labeling. Barbell graph B n is obtained by connecting two copies of a complete graph Kn by a bridge. In this research, we determined the total edge irregularity strength of barbell graph Bn for n ≥ 3.

Journal of The International Mathematical Virtual Insitute, 2019

An edge irregular total k-labeling f : V ∪ E → {1, 2, 3, . . . , k} ofa graph G = (V, E) is a labeling of vertices and edges of G in such a way thatfor any two different edges uv and u′v′ their weights f (u) + f (uv) + f (v) andf (u′) + f (u′v′) + f (v′) are distinct. The total edge irregularity strength tes(G)is defined as the minimum k for which the graph G has an edge irregular totalk-labeling. In this paper, we study the total edge irregularity strength forshadow graph of cycle and path, total graph of cycle and path, lotus inside acircle, double wheel graph (

Indonesian Journal of Combinatorics, 2020

Under a totally irregular total k-labeling of a graph G = (V, E), we found that for some certain graphs, the edge-weight set W (E) and the vertex-weight set W (V) of G which are induced by k = ts(G), W (E) ∩ W (V) is a nonempty set. For which k, a graph G has a totally irregular total labeling if W (E) ∩ W (V) = ∅? We introduce the total disjoint irregularity strength, denoted by ds(G), as the minimum value k where this condition satisfied. We provide the lower bound of ds(G) and determine the total disjoint irregularity strength of cycles, paths, stars, and complete graphs.

An edge irregular total k-labeling f : V ∪ E → {1, 2, 3, . . . , k} of a graph G = (V, E) is a labeling of vertices and edges of G in such a way that for any two different edges uv and u

Mathematics in Computer Science, 2015

A total k-labeling is a map that carries vertices and edges of a graph G into a set of positive integer labels {1, 2, ..., k}. An edge irregular total k-labeling of a graph G is a total k-labeling such that the weights calculated for all edges are distinct. The weight of an edge uv in G is defined as the sum of the label of u, the label of v and the label of uv. The total edge irregularity strength of G, denoted by tes(G), is the minimum value of the largest label k over all such edge irregular total k-labelings. In this paper, we investigate the total edge irregularity strength of generalized helm, H m n for n ≥ 3, m = 1, 2, and m ≡ 0 (mod 3).

International Journal of Pure and Apllied Mathematics, 2015

Given a graph G(V, E) a labeling ∂ : V ∪ E → {1, 2, ..., k} is called an edge irregular total k-labeling if for every pair of distinct edges uv and xy, The minimum k for which G has an edge irregular total k -labeling is called the total edge irregularity strength. In this paper we consider series composition of uniform theta graphs and obtain its total edge irregularity strength. We have determined the exact value of the total edge irregularity strength of this graph. We have further given an algorithm to prove the result.