Ordering chemical graphs by Randić and sum-connectivity numbers

Abstract Let G be a graph with edge set E(G). The Randic and sum-connectivity indices of G are defined as R ( G ) = ∑ u v ∈ E ( G ) 1 d e g G ( u ) d e g G ( v ) and S C I ( G ) = ∑ u v ∈ E ( G ) 1 d e g G ( u ) + d e g G ( v ) , respectively, where degG(u) denotes the vertex degree of u in G. In this paper, the extremal Randic and sum-connectivity index among all n-vertex chemical trees, n ≥ 13, connected chemical unicyclic graphs, n ≥ 7, connected chemical bicyclic graphs, n ≥ 6 and connected chemical tricyclic graphs, n ≥ 8, were presented.