# $d_2$-coloring of a Graph

Volume 3, Issue 2, pp 102--111
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### Authors

K. Selvakumar - Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627 012, Tamil Nadu, India S. Nithya - Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627 012, Tamil Nadu, India

### Abstract

A subset S of V is called an i-set ($i\geq 2$) if no two vertices in S have the distance i. The 2-set number $\alpha_2(G)$ of a graph is the maximum cardinality among all 2-sets of G. A $d_2$-coloring of a graph is an assign- ment of colors to its vertices so that no two vertices have the distance two get the same color. The $d_2$-chromatic number $\chi_{d_2}(G)$ of a graph G is the minimum number of $d_2$-colors need to G. In this paper, we initiate a study of these two new parameters.

### Keywords

• $d_2$-coloring
• $d_2$-chromatic number

•  05C15

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