On the maximal general ABC index of graphs with given maximum degree

Abstract

The atom-bond connectivity index ABC is a topological index that has recently found remarkable applications in the study of the strain energy of cycloalkanes as well as in rationalizing the stability of linear and branched alkanes. In order to improve the correlation properties of the atom-bond connectivity index for the heat of formation of alkanes, Furtula et al. considered a generalization of this index, namely, ABCα = ABCα (G) = uv∈E(G) du + dv − 2 dudv α for any α ∈ R \ {0}, where dv is the degree of the vertex v and uv denotes the edge connecting the vertices u and v of graph G. Here, we obtain some optimization results for ABCα of the connected graph G.