On the total edge irregularity strength of generalized helm. (English) Zbl 1301.05295
Summary: A total \(k\)-labeling is a map that carries vertices and edges of a graph \(G\) into a set of
positive integer labels \(\{1, 2,\dots, k\}\). An edge irregular total \(k\)-labeling of a graph \(G\) is a total \(k\)-labeling such that the weights calculated for all edges are distinct. The weight of an edge
\(uv\) in \(G\) is defined as the sum of the label of \(u\), the label of \(v\) and the label of \(uv\). The total
edge irregularity strength of \(G\), denoted by \(\mathrm{tes}(G)\), is the minimum value of the largest label \(k\) over all such edge irregular total \(k\)-labelings. In this paper, we investigate the total edge irregularity strength of generalized helm, \(H^m_n\) for \(n\geq 3\), \(m = 1, 2\), and \(m\equiv 0 \pmod 3\).
MSC:
05C78 | Graph labelling (graceful graphs, bandwidth, etc.) |