On the total version of geometric-arithmetic index, pp

A single number that can be used to characterize some property of the graph of a molecule is called a topological index for that graph. There are numerous topological descriptors that have found some applications in theoretical chemistry, especially in QSPR/QSAR research [7]. The oldest topological index which introduced by Harold Wiener in 1947 is ordinary (vertex) version of Wiener index [9] which is the sum of all distances between vertices of a graph. Also, the edge versions of Wiener index which were based on distance between edges introduced by Iranmanesh et al. in 2008 [3]. One of the most important topological indices is the well-known branching index introduced by Randić [6] which is defined as the sum of certain bond contributions calculated from the vertex degree of the hydrogen suppressed molecular graphs.