ON THE EDGE VERSION OF GEOMETRIC-ARITHMETIC INDEX

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 [1]. The oldest topological index which introduced by Harold Wiener in 1947 is ordinary (vertex) version of Wiener index [2] 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 Randic [4] which is defined as the sum of certain bond contributions calculated from the vertex degree of the hydrogen suppressed molecular graphs. Motivated by the definition of Randic connectivity index based on the end-vertex degrees of edges in a graph connected G with the vertex set ( ) V G and the edge set ( ) E G [5,6], Vukicevic and Furtula [7] proposed a topological index named the geometric-arithmetic index (shortly GA) as