Let [Formula: see text] be a simple graph with vertex set [Formula: see text] and edge set [Formula: see text], respectively. An edge irregular [Formula: see text]-labeling of [Formula: see text] is a labeling of [Formula: see text] with labels from the set [Formula: see text] in such a way that for any two different edges [Formula: see text] and [Formula: see text], their weights [Formula: see text] and [Formula: see text] are distinct. The weight of an edge [Formula: see text] in [Formula: see text] is the sum of the labels of the end vertices [Formula: see text] and [Formula: see text]. The minimum [Formula: see text] for which the graph [Formula: see text] has an edge irregular [Formula: see text]-labeling is called the edge irregularity strength of [Formula: see text], denoted by [Formula: see text]. In this paper, we determine the exact value of edge irregularity strength of corona product of graphs with cycle.

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<abstract><p>Graph labeling is an assignment of (usually) positive integers to elements of a graph (vertices and/or edges) satisfying certain condition(s). In the last two decades, graph labeling research received much attention from researchers. This articles is about edge irregularity strength for some classes of plane graphs. Edge irregularity strength denoted by $ es(G) $, was introduced by Ahmad et al. in 2014 as a modification of the well known irregularity strength by Chartrand in 1988. In this paper, the exact value of the edge irregularity strength for some clases of plane graphs is determined.</p></abstract>

For a simple graph G, a vertex labeling φ : V (G) → {1, 2, . . . , k} is called a vertex k-labeling. For any edge x y in G, its weight w φ (x y) = φ(x) + φ(y). If all the edge weights are distinct, then φ is called an edge irregular k-labeling of G. The minimum k for which the graph G has an edge irregular k-labeling is called the edge irregularity strength of G, denoted by es(G).In this paper, we determine an exact value of edge irregularity strength for triangular grid graph L m n , zigzag graph Z m n and Cartesian product P n □P m □P 2 .

With respect to a simple graph G, a vertex labeling ϕ: V(G) > {1,2,...,k) is known as k-labeling. The weight corresponding to an edge xy in G, expressed as wϕ (xy), represents the labels sum of end vertices x and y, given by wϕ (xy) = ϕ(x) + ϕ(y) A vertex k-labeling is expressed as an edge irregular k-labeling with respect to graph G provided that for every two distinct edges e and f, there exists wϕ(e) ≠ wϕ(f) Here, the minimum k where the graph G possesses an edge irregular k-labeling is known as the edge irregularity strength with respect to G, expressed as (G). Here, we examine the edge irregularity strength’s exact value of corona product with respect to two paths Pn and Pm , in which n ≥ 2 and m = 3, 4, 5.