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

Abstract

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 $e=e_1{e}_2$ and $f=f_1{f}_2$ in $E(G)$ we have $wt(e)\ne wt(f)$ 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.