Diameter of 2-distance graphs

For a simple graph G, the 2-distance graph, D₂ (G), is a graph with the vertex set V (G) and two vertices are adjacent if and only if their distance is 2 in the graph G. In this paper, for graphs G with diameter 2, we show that diam (D₂ (G) ) can be any integer t2. For graphs G with diam (G) 3, we prove that 12diam (G) diam (D₂ (G) ) and this inequality is sharp. Also, for diam (G) =3, we prove that diam (D₂ (G) ) 5 and this inequality is sharp.