On the total edge irregularity strength of general uniform cactus chain graphs with pendant vertices. (English) Zbl 1482.05302
Summary: Let \(G(V, E)\) be a graph. Throughout this paper, we use the notions of edge irregular total \(k\)-labeling and total edge irregularity strength of \(G\) (\(\mathrm{tes}\ (G)\)). We verify tes of general uniform cactus chain graphs \(C_r(C^{n-2}_n)\) having \((n-2)r\) pendant vertices and length \(r\). The result obtained is as follows: \(tes(C_r(C^{n-2}_n)=\lceil\frac{(2n-2)r+2}{3}\rceil\) for \(n\geq 6\).
MSC:
| 05C78 | Graph labelling (graceful graphs, bandwidth, etc.) |
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