## Abstract

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,..., 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 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_{n} ^{m} for n ≥ 3, m = 1, 2, and m ≡ 0 (mod 3).

Original language | English |
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Pages (from-to) | 147-155 |

Number of pages | 9 |

Journal | AKCE International Journal of Graphs and Combinatorics |

Volume | 10 |

Issue number | 2 |

Publication status | Published - 1 Aug 2013 |

## Keywords

- Edge irregular total k-labeling
- Generalized helm
- Total edge irregularity strength
- Total k-labeling