Balaban Index of Dendrimers A. R. Ashrafi a , H. Shabani a , M. V. Diudea b,  a Department of Mathematics, Statistics and Computer Science, Faculty of Science, University of Kashan, Kashan 87317-51167, I. R. Iran b Faculty of Chemistry and Chemical Engineering, “Babes-Bolyai” University, 400028 Cluj, Romania (Received June 5, 2010) Abstract The Balaban index of a graph is the sum of the terms m/(+1)[d(x)d(y)] -0.5 over all edges e = xy, where  is the cyclomatic number of G and for every vertex x of G, d(x) denotes the summation of distances between x and all vertices of G. In this article, the Balaban index of a class D k of dendrimers is computed by a group theoretical method. It shows that the Balaban index of a sequence x n can be decreased strictly, when n is increased. 1. Introduction Dendrimers are generally described as a macromolecule, which is built from a starting atom, such as nitrogen, to which carbon and other elements are added by a repeating series of chemical reactions that produce a spherical branching structure. In a divergent synthesis of a dendrimer, one starts from the core (a multi connected atom or group of atoms) and growths out to the periphery. In each repeated step, a number of monomers are added to the actual structure, in a radial manner, in resulting quasi-concentric shells, called generations. In a convergent synthesis, the periphery is first built up and next the branches (called dendrons) are connected to the core. These rigorously tailored structures reach rather soon (between the thirds to tenth generation, depending on the number of connections less than three between the branching points, i.e., connections equal or higher than three, along the rays of the molecular star) a spherical shape, which resembles that of a globular protein, after that the  Corresponding author Email address: diudea@gmail.com MATCH Communications in Mathematical and in Computer Chemistry MATCH Commun. Math. Comput. Chem. 69 (2013) 151-158 ISSN 0340 - 6253