The Total Edge-irregular Strengths of the Corona Product of Paths with Some Graphs

For a simple graph \( G = (V(G), E(G)) \) with the vertex set \( V(G) \) and the edge set \( E(G) \), a labeling \( \lambda: V(G) \cup E(G) \to \{1, 2, \dots, k\} \) is called an edge-irregular total \( k \)-labeling of \( G \) if for any two different edges \( e = e_1e_2 \) and \( f = f_1f_2 \) in \( E(G) \) we have \( wt(e) \neq wt(f) \) where \( wt(e) = \lambda(e_1) + \lambda(e) + \lambda(e_2) \). The total edge-irregular strength, denoted by \( tes(G) \), is the smallest positive integer \( k \) for which \( G \) has an edge-irregular total \( k \)-labeling. In this paper, we determine the total edge-irregular strength of the corona product of paths with some graphs.