Further results on edge irregularity strength of graphs

Muhammad Imran, Adnan Aslam, Sohail Zafar, Waqas Nazeer

Abstract


A vertex $k$-labelling $\phi:V(G)\longrightarrow \{1,2,\ldots,k\}$ is called irregular $k$-labeling of the graph $G$ if for every two different edges $e$ and $f$, there is $w_{\phi}(e)\neq w_{\phi}(f)$; where the weight of an edge is given by $e=xy\in E(G)$ is $w_{\phi}(xy)=\phi(x)+\phi(y)$. The minimum $k$ for which the graph $G$ has an edge irregular $k$-labelling is called \emph{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.


Keywords


irregular assignment, irregular total k-labeling, irregularity strength

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DOI: http://dx.doi.org/10.19184/ijc.2017.1.2.5

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