chapter  Chapter 19
22 Pages

Geometric-Arithmetic Index

WithMahdieh Azari, Ali Iranmanesh

Mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of molecular structures using mathematical methods without necessarily referring to quantum mechanics. Chemical graph theory is a branch of mathematical chemistry which applies graph theory to mathematical modeling of chemical phenomena. The GA index was first introduced in a paper by Vukicevic and Furtula published in the Journal of Mathematical Chemistry as one of the successors of the Randic connectivity index. This index was named as geometric-arithmetic index, it consists of a geometrical mean of end-vertex degrees of an edge uv, dudv, as numerator and arithmetic mean of end-vertex degrees of the edge uv, (du + dv)/2, as denominator. A descriptor is called degenerate if it possesses the same value for more than one graph. Dehmer et al. evaluated the uniqueness, discrimination power or degeneracy of some degree, distance, and eigenvalue-based descriptors for investigating graphs holistically.