Ibrahim, M.; Asif, M.; Ahmad, A.; Siddiqui, M. K. Computing the total irregularity strength of wheel related graphs. (English) Zbl 1407.05203 Util. Math. 108, 321-338 (2018). 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.) Keywords:irregularity strength; total edge irregularity strength; total irregularity strength; totally irregular total \(k\)-labeling; wheel related graphs PDFBibTeX XMLCite \textit{M. Ibrahim} et al., Util. Math. 108, 321--338 (2018; Zbl 1407.05203)