## Abstract

For a simple graph G, a vertex labeling f: V (G) → (1; 2....,k) is called a k-labeling. The weight of a vertex v, denoted by wt_{f} (v) is the sum of all vertex labels of vertices in the closed neighborhood of the vertex v. A vertex k-labeling is defined to be an inclusive distance vertex irregular distance k-labeling of G if for every two different vertices u and v there is wt_{f} (u) ≠ wt_{f} (v). The minimum k for which the graph G has a vertex irregular distance k-labeling is called the inclusive distance vertex irregularity strength of G. In this paper we establish a lower bound of the inclusive distance vertex irregularity strength for any graph and determine the exact value of this parameter for several families of graphs.

Original language | English |
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Pages (from-to) | 61-83 |

Number of pages | 23 |

Journal | Electronic Journal of Graph Theory and Applications |

Volume | 6 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

## Keywords

- Inclusive distance vertex irregular labeling
- Inclusive distance vertex irregularity strength