## Abstract

Let G be a simple, connected and undirected graph with vertex set V and edge set E. A total k-labeling f : V ∪ E → {1, 2, ⋯, k} is defined as totally irregular total k-labeling if the weights of any two different both vertices and edges are distinct. The weight of vertex x is defined as wt(x) = f(x) + ∑_{xy∈E} f(xy), while the weight of edge xy is wt(xy) = f(x) + f(xy) + f(y). A minimum k for which G has totally irregular total k-labeling is mentioned as total irregularity strength of G and denoted by ts(G). This paper contains investigation of totally irregular total k-labeling for caterpillar graphs S_{n,2,m} and determination of their total irregularity strengths. In addition, the total vertex and total edge irregularity strength of this graph also be determined. The results are tvs(S_{n;2;m}) = ⌈n+m-1/2⌉, tes(S_{n;2;m}) =⌈n+m+2/3⌉ and ts(S_{n;2;m}) = ⌈n+m-1/2⌉for n, m ≥ 3.

Original language | English |
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Article number | 012018 |

Journal | Journal of Physics: Conference Series |

Volume | 855 |

Issue number | 1 |

DOIs | |

Publication status | Published - 12 Jun 2017 |

Event | 1st International Conference on Mathematics: Education, Theory, and Application, ICMETA 2016 - Surakarta, Indonesia Duration: 6 Dec 2016 → 7 Dec 2016 |