Note on two generalizations of the Randic index

For a given graph G, the well-known Randic index of G, introduced by Milan Randic in 1975, is defined as R(G) = Sigma(uv is an element of E)(d(u),d(v))(-1/2). where the sum is taken over all edges uv and d(u), denotes the degrees of u. Bolloba's and Erdos generalized this index by replacing -1/2 with any real number alpha, which is called the general Randic index. Dvorak et al. introduced a modified version of Randic index: R'(G) = Sigma(uv is an element of E)(G) (max {d(u), d(v)}(-1). Based on this, recently, Knor et al. introduced two generalizations: R'(alpha)(G) = Sigma min {d(u)(alpha), d(v)(alpha)} and R"(alpha)(G) = Sigma max {d(u)(alpha), d(v)(alpha)} uv is an element of(G) uv is an element of(G) for any real number alpha. Clearly, the former is a lower bound for the general Randic' index, and the latter is its upper bound. Knor et al. studied extremal values of R'alpha(G) R"alpha (G) and and concluded some open problems. In this paper, we consider the open problems and give some comments and results. Some results for chemical trees are obtained. (C) 2015 Elsevier Inc. All rights reserved.