## SOME RESULTS ON THE DISTANCE r-b-COLORING IN GRAPHS

*G. JOTHILAKSHMI , A. P. PUSHPALATHA , S. SUGANTHI , V. SWAMINATHAN *

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## Abstract

Given a positive integer r, two vertices u; v 2 V (G) are r- independent if d(u; v) > r. A partition of V (G) into r-independent sets is called a distance r-coloring. A study of distance r-coloring and distance r-b-coloring concepts are studied in this paper.

## Keywords

distance r-chromatic number, distance r-independent color partition, distance r-independent set, distance r-b-coloring number.