General Randić index of unicyclic graphs with given diameter

Abstract We study the general Randic index R a ( G ) = ∑ u v ∈ E ( G ) [ d e g G ( u ) d e g G ( v ) ] a , where a ∈ R , E ( G ) is the edge set of a graph G , and d e g G ( u ) and d e g G ( v ) are the degrees of vertices u and v , respectively. For a set of unicyclic graphs of given order and diameter, we present the unique graph having the minimum general Randic index, where − 0 . 64 ≤ a 0 . Since R − 1 2 ( G ) is the Randic index of a graph G , our result holds also for the classical Randic index.