## Abstract

A total vertex irregularity strength of a graph G, tvs(G), is the minimum positive integer k such that there is a mapping f from the union of vertex and edge sets of G to {1, 2, ⋯, k} and the weights of all vertices are distinct. The weight of a vertex in G is the sum of its vertex label and the labels of all edges that incident to it. It is known that tvs(K_{n}) = 2. In this paper, we construct graphs with tvs equal to 2 by removing as much as possible edges from Kn, with and without maintaining the outer cycle Cn of K_{n}. To do so, we give two algorithms to construct the graphs, and show that the tvs of the resulting graph is equal to 2.

Original language | English |
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Pages (from-to) | 132-137 |

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

- algorithm
- complete graph
- cycle
- Total vertex irregularity strength