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Sohail Zafar
Department of Mathematics University of Management and Technology, Lahore, Pakistan
Computer Science & IT Decision Sciences, Operations Research & Management

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Further results on edge irregularity strength of graphs Muhammad Imran; Adnan Aslam; Sohail Zafar; Waqas Nazeer
Indonesian Journal of Combinatorics Vol 1, No 2 (2017)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (183.847 KB) | DOI: 10.19184/ijc.2017.1.2.5

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.
Co-Authors Adnan Aslam Muhammad Imran Waqas Nazeer