Dendrimers are large and complex molecules with very well-defined chemical structures. From a polymer chemistry point of view, dendrimers are nearly perfect monodisperse (basically meaning of a consistent size and form) macromolecules with a regular and highly branched three-dimensional architecture. They consist of three major architectural components: core, branches and end groups. In chemical graph, each vertex represented an atom of the molecule, and covalent bonds between atoms are represented by edges between the corresponding vertices. This shape derive from a chemical compound is often called its molecular graph.
Let e be an edge of a G connecting the vertices u and v. Define two sets N1(e|G) and N2(e|G) as N1(e|G)={x?V(G)d(x, u)<d(x, v)} and N2(e|G)={x?V(G)|d(x, u)}., the number of elements of N1(e|G) and N2(e|G) are denoted by n1(e|G) and n2(e|G) respectively. The Szeged index of the graph G is defined as Sz(G)=?e?En1(e|G)n2(|G). In this thesis we compute the szeged index of some dendrimer nanostars.