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\iteman{io-port 06121768}
\itemau{Siddiqui, Muhammad Kamran}
\itemti{On total edge irregularity strength of categorical product of cycle and path.}
\itemso{AKCE Int. J. Graphs Comb. 9, No. 1, 43-52 (2012).}
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Summary: We investigate a modification of well known irregularity strength of graph, namely the total edge irregularity strength. An edge irregular total $k$-labeling $\phi\colon V\cup E\to\{1,2,\dots,k\}$ of a graph $G$ is a labeling of vertices and edges of $G$ in such a way that for any two different edges $uv$ and $u'v'$ their weights $\phi(u)+\phi(uv)+\phi(v)$ and $\phi(u')+\phi(u'v')+\phi(v')$ are distinct. The total edge irregularity strength, $tes(G)$, is defined as the minimum $k$ for which $G$ has an edge irregular total $k$-labeling. The main purpose of this paper is to solve the open problem posed by {\it A. Ahmad} and {\it M. Ba\v ca} [ibid. 6, No. 1, 21--29 (2009; Zbl 1210.05130)].
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