On edge irregularity strength of subdivision of star Sn

In this paper, we study the total edge irregularity strength of some well known graphs. An edge irregular total $k$-labeling $varphi: Vcup E o { 1,2, dots, k }$ 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 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. Also, we determine the exact value of the total edge irregularity strength of subdivision of star $S_n.$