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
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.