## Abstract

Let G = (V, E) be a simple and undirected graph with a vertex set V and an edge set E. A totally irregular total k-labeling f: V ∩ E → {1, 2,⋯, k} is a labeling of vertices and edges of G in such a way that for any two different vertices x and x1, their weights wt_{f}(x) = f(x) + ∑_{xyεE} f(xy) and wt_{f}(x′) = f(x′) + ∑_{xyεE} f(x′y′)are distinct, and for any two different edges xy and x1y1 their weights f (x) + f (xy) + f (y) and f (x1) + f (x1y1) + f (y1) are also distinct. A total irregularity strength of graph G, denoted byts(G), is defined as the minimum k for which G has a totally irregular total k-labeling. In this paper, we determine the exact value of the total irregularity strength for double-star S_{n,m}, n, m ≥ 3 and graph related to it, that is a caterpillar S_{n,2,n}, n ≥ 3. The results are and ts(S_{n,2,n}) = [n+m-1/2] ts(S_{n,2,n})n.

Original language | English |
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Pages (from-to) | 118-123 |

Number of pages | 6 |

Journal | Procedia Computer Science |

Volume | 74 |

DOIs | |

Publication status | Published - 1 Jan 2015 |

Event | 2nd International Conference of Graph Theory and Information Security, 2015 - Bandung, Indonesia Duration: 21 Sep 2015 → 23 Sep 2015 |

## Keywords

- caterpillar
- double-star
- total irregularity strength
- Totally irregular total k-labeling
- weight