Further results on edge irregularity strength of graphs - Muhammad Imran; Adnan Aslam; Sohail Zafar; Waqas Nazeer (Indonesian Journal of Combinatorics, 2017)
A vertex $k$-labelling $φ:V(G)\longrightarrow \{1,2,…,k\}$ is called irregular $k$-labeling of the graph $G$ if for every two different edges $e$ and $f$, there is $w_{φ}(e)≠ w_{φ}(f)$; where the weight of an edge is given by $e=xy\in E(G)$ is $w_{φ (xy)=φ(x)+φ(y)$. The minimum $k$ for which the graph $G$ has an edge irregular $k$-labelling is called edge irregularity strength of $G$, denoted by $es(G)$. In the paper, we determine the exact value of the edge irregularity strength of caterpillars, $n$-star graphs, $(n,t)$-kite graphs, cycle chains and friendship graphs.