A note on edge irregularity strength of Dandelion graph

For a simple graph $G$, a vertex labeling $\phi :V(G)\to \{1,2,\dots ,k\}$ is called $k$-labeling. The weight of an edge $xy$ in $G$, written $w_{\phi }(xy)$, is the sum of the labels of end vertices $x$ and $y$, i.e., $w_{\phi }(xy)=\phi (x)+\phi (y)$. A vertex $k$-labeling is defined to be an edge irregular $k$-labeling of the graph $G$ if for every two different edges $e$ and $f$, $w_{\phi }(e)\mathrm{\ne }{w}_{\phi }(f)$. The minimum $k$ for which the graph $G$ has an edge irregular $k$-labeling is called the edge irregularity strength of $G$, written $es(G)$. In this note, we find the exact value of edge irregularity strength of Dandelion graph when $\mathrm{\Delta }(G)\ge \lceil \frac{\mathrm{\mid }E(G)\mathrm{\mid }+1}{2}\rceil$; and determine the bounds when $\mathrm{\Delta }(G)<\lceil \frac{\mathrm{\mid }E(G)\mathrm{\mid }+1}{2}\rceil$.