علیرضا عطایی

Dendrimers are repetitively branched molecules. The name "Dendrimer" comes from the Greek word "Dendron" which translates to "tree" and the suffix "Mer" that means part. In general, dendrimers includes core, dendrimer generations and terminal surface groups. Each group of these molecules has many similar properties. One kind of these dendrimers that have regular graph are called regular Dendrimers. Since computing the functional applied properties of chemical molecules in large-scale is difficult, we used a mathematical model of molecular graphs topological polynomials and indices to study some properties of this group of molecules. In this thesis, first we calculate some topological polynomials and indices of regular Dendrimers,like Padmakar – Ivan, Eccentric connectivity, Randic, Second Zagreb, Modified Second Zagreb and all Geometric-Arithmetic polynomials and indices. Finally, we compute all geometric-arithmetic polynomials and indices of regular dendrimers, then establish some bounds for them indices.