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 is the degree of the vertex vi of G and ? arbitrary real number. We consider linear combinations of the 0R?(G) of the form 0R?(G) ? (? + ?)0R??1(G) + ?? 0R??2(G) and 0R?(G) ? 2a 0R??1(G) + a2 0R??2(G), where a is an arbitrary real number, and determine their bounds. As corollaries, various upper and lower bounds of 0R?(G) and indices that represent some special cases of 0R?(G) are obtained.