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Computing the total irregularity strength of wheel related graphs. (English) Zbl 1407.05203

Summary: Let \(G= (V,E)\) be a graph. A total labeling \(\phi: V\cup E\to\{1,2,\dots, k\}\) is called totally irregular total \(k\)-labeling of \(G\) if every two distinct vertices \(x\) and \(y\) in \(V(G)\) satisfies \(wt(x)\neq wt(y)\), and every two distinct edges \(xy\) and \(x'y'\) in \(E(G)\) satisfies \(wt(xy)\neq wt(x'y')\), where \[ wt(x)= \phi(x)+ \sum_{xz\in E(G)} \phi(xz)\text{ and }wt(x)= \phi(x)+ \phi(xy)+ \phi(y). \] The minimum \(k\) for which a graph \(G\) has a totally irregular total \(k\)-labeling is called the total irregularity strength of \(G\), denoted by \(ts(G)\).
In this paper, we compute the total irregularity strength of wheel related graphs.

MSC:

05C78 Graph labelling (graceful graphs, bandwidth, etc.)
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