On atom-bond connectivity index

The atom-bond connectivity index (ABC) is a molecular structure descriptor that recently found a remarkable application in rationalizing the stability of linear and branched alkanes as well as the strain energy of cycloalkanes. Let G be a molecular graph, di the degree of its vertex i, and ij the edge connecting the vertices i and j. Then ABC = ∑ ij ( d i + d i - 2 ) / ( d i d j ) . Several properties of ABC are established. In particular, if a new edge is inserted into G, then ABC necessarily increases. By means of this result we characterize the graphs extremal w.r.t. ABC.