A note on edge irregularity strength of Dandelion graph

For a simple graph G, a vertex labeling φ:V(G) → \1, 2,…,k\ is called k-labeling. The weight of an edge $xy$ in G, written wφ(xy), is the sum of the labels of end vertices x and y, i.e., wφ(xy)=φ(x)+φ(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, wφ(e) ≠ wφ(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 Δ(G) ≥ |E(G)|+1/2; and determine the bounds when Δ(G) < |E(G)|+1/2.