Some Basic Results on the Second Multiplication Atom-Bond Connectivity Index

Abstract

As the atom-bond connectivity index kept expanding, the multiplicative atom-bond connectivity indices were introduced to measure the stability of alkanes and strain energy of cycloalkanes. Let ABCΠ(G) = uv∈E(G) nu+nv −2 nunv denote the first multiplicative atom-bond connectivity index (ABCΠ) of a graph G, in which nu represents the number of vertices which are closer to vertex u than vertex v. Similarly, nv is defined in this way. In this paper, we study the basic mathematical characters of the second multiplicative atom-bond connectivity index.