The atom-bond connectivity index of chemical bicyclic graphs

The atom-bond connectivity (ABC) index provides a good model for the stabilityof linear and branched alkanes as well as the strain energy of cycloalkanes,which is defined as ABC(G) =Σuv∈(G)√ du +dv - 2/dudv,where du denotes the degree of a vertex u in G.A chemical graph is a graph in which no vertex has degree greater than 4.In this paper,we obtain the sharp upper and lower bounds on ABC index of chemical bicyclic graphs.