On the bounds of zeroth-order general Randic index

The zeroth-order general Randic index, 0R?(G), of a connected graph G, is defined as 0 P R?(G) = ni =1 d?i , where di the degree vertex vi G and ? arbitrary real number. We consider linear combinations 0R?(G) form (? + ?)0R??1(G) ?? 0R??2(G) 2a 0R??1(G) a2 0R??2(G), an number, determine their bounds. As corollaries, various upper lower bounds indices that represent some special cases are obtained.