Some remarks on the general zeroth-order Randic coindex

Abstract

Let G = (V, E), V = {v1, v2,..., vn}, be a simple connected graph of order n and size m, without isolated vertices. Denote by d1 ? d2 ?... ? dn, di = d(vi) a sequence of vertex degrees of G. The general zeroth-order Randic index is defined as 0R?(G) = ?ni =1 d?i, where ? is an arbitrary real number. The corresponding general zeroth-order Randic coindex is defined via 0R??(G) = ?ni=1(n?1?di)d?i. Some new bounds for the general zeroth-order Randic coindex and relationship between 0R??(G?) and 0R???1(G?) are obtained. For a particular values of parameter ? a number of new bounds for different topological coindices are obtained as corollaries.