## Abstract

We define the r-dynamic local irregularity vertex coloring. Suppose λ: V(G) → {1,2, …, k} is called vertex irregular k-labeling and w: V(G) → N where (formula presented). λ is called r-dynamic local irregular vertex coloring, if: (i) opt(λ) = min{max{λi}; λ_{i} vertex irregular k-labeling}, (ii) for every uv Є E(G), w(u) ≠ w(v), and (iii) for every v Є V(G) such that |w(N(v))| ≥ min{r, d(v)}. The chromatic number r-dynamic local irregular denoted by (formula presented), is minimum of cardinality r-dynamic local irregular vertex coloring. We study the r-dynamic local irregularity vertex coloring of graph and we have found the exact value of chromatic number r-dynamic local irregularity of some graph.

Original language | English |
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Pages (from-to) | 767-769 |

Number of pages | 3 |

Journal | International Journal of Scientific and Technology Research |

Volume | 8 |

Issue number | 7 |

Publication status | Published - Jul 2019 |

## Keywords

- Local irregularity
- R-dynamic coloring
- Vertex coloring