### Abstract

The d-distance coloring of G (V, E) is an assignment of {1, 2, …, k} colors to the vertices such that any two vertices within distance d receive different colors. If the set of vertices of a graph G can be partitioned into k classes V_{1}, V_{2}, V_{3} …, V_{k}, such that ||V_{i}|-|V_{j}|| for any, 1 ≤ i, j ≤ k, then G is said to be equitably k-colorable. In this paper, we introduce d-distance equitable coloring and obtain d-distance equitable chromatic number for cycle. Also, we present linear time an algorithm for d-distance coloring of trees and (Formula Presented) time an algorithm for d-distance equitable coloring.

Original language | English |
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Pages (from-to) | 2140-2150 |

Number of pages | 11 |

Journal | International Journal of Advanced Science and Technology |

Volume | 29 |

Issue number | 5 |

Publication status | Published - 10-04-2020 |

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### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Engineering(all)
- Energy(all)

### Cite this

*International Journal of Advanced Science and Technology*,

*29*(5), 2140-2150.