Computing the Szeged Index of Two Type Dendrimer Nanostars

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Computing the Szeged Index of Two Type Dendrimer Nanostars

Croatian Chemical Society
  • Wiener Index
  • Szeged Index
  • Dendrimer Nanostars


iranmanes.vp Computing the Szeged Index of Two Type Dendrimer Nanostars Ali Iranmanesha and Nabi Allah Gholamib a Department of Mathematics, Faculty of Science, Tarbiat Modares University, P. O. Box 14115-137, Tehran, Iran b Academic Center for Education, Culture and Research TMU, P. O. Box 14115-343, Tehran, Iran RECEIVED JANUARY 22, 2008; REVISED MARCH 1, 2008; ACCEPTED MARCH 3, 2008 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,v) < 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∈∑ E n1(e |G) n2(e |G). In this paper we compute the szeged index of the first and second type of dendrimer nanostar. Keywords dendrimer nanostars Szeged index Wiener index CROATICA CHEMICA ACTA CCACAA 81 (2) 299¿303 (2008) ISSN-0011-1643 CCA-3244 Original Scientific Paper INTRODUCTION Dendrimers are large and complex molecules with very well-defined chemical structures. From a polymer chem- istry 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. Dendrimers are produced in an iterative sequence of reaction steps.1 We can consider the figure of dendrimers as the shape of molecular graph. A graph G consist of a set of vertices V(G) and a set of edges E(G). In chemical graph, each vertex repre- sented an atom of the molecule, and covalent bonds be- tween atoms are represented by edges between the cor- responding vertices. This shape derive from a chemical compound is often called its molecular graph, and can be a path, a tree or in general a graph. A topological index is a single number, derived

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