## Abstract

A vertex irregular total labeling φ of a graph G is a labeling of vertices and edges of G with labels from the set {1, 2, ⋯, K} in such a way that for any two different vertices x and y their weights wt(x) and wt(y) are distinct. The weight wt(x) of a vertex x in G is the sum of its label and the labels of all edges incident with a given vertex x. The minimum fc for which the graph G has a vertex irregular total labeling is called the total vertex irregularity strength of G, tvs(G). In this paper, we determine exact value of the toted vertex irregularity strength of cubic graphs and a conjecture is proposed to find tvs of r-reguleir graphs.

Original language | English |
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Pages (from-to) | 287-299 |

Number of pages | 13 |

Journal | Utilitas Mathematica |

Volume | 91 |

Publication status | Published - Jul 2013 |

Externally published | Yes |

## Keywords

- Convex polytopes
- Cubic plane graph
- Total vertex irregularity strength
- Vertex irregular total labeling
- Vertex weight

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics