The Wiener index of a graph G is defined as W(G) = 1/2∑{x,y}⊆V(G)d(x,y), where V(G) is the set of all vertices of G and for x,y ∈ V(G), d(x,y) denotes the length of a minimal path between x and y. In this paper, we first report our recent results on computing Wiener, PI and Balaban indices of some nanotubes and nanotori. Next, the PI and Szeged indices of a new type of nanostar dendrimers are c...

The edge Szeged polynomial of a graph G is defined as Sze(G,x) = ( ) ( ) , u v m e m e e uv x = ∑ where mu(e) is the number of edges of G lying closer to u than to v and mv(e) is the number of edges of G lying closer to v than to u. In this paper the main properties of this newly proposed polynomial are investigated. We also compute this polynomial for some classes of well-known graphs. Finally...

Clear indication has it in numerous studies that a strong inherent relationship exists between the chemical characteristics of chemical compounds and drugs (e.g., boiling point and melting point) and their molecular structures. There are several topological indices are defined on these chemical molecular structures and they can help researchers better understand the physical features, chemical ...

Dendrimers are highly branched organic macromolecules with successive layers or generations of branch units surrounding a central core [1,4]. These are key molecules in nanotechnology and can be put to good use. In this article, we compute the first geometricarithmetic index of two infinite classes of dendrimers.