On molecular topological properties of dendrimers

Abstract

Topological indices are numerical parameters of a graph that characterize its topology and are usually graph invariant. In a QSAR/QSPR study, physicochemical properties and topological indices such as the Randić, atom–bond connectivity (ABC), and geometric–arithmetic (GA) indices are used to predict the bioactivity of different chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study the degree-based molecular topological indices such as ABC4 and GA5 for certain families of dendrimers. We derive the analytical closed formulae for these classes of dendrimers.

On Topological Indices of Certain Families of Nanostar Dendrimers

“…The structure-sensitivity of degree-based molecular topological indices has been discussed in detail in [22]. and indices for some families of nanostar dendrimers and polyphenylene dendrimers are discussed in [20,21,24]. For a detailed description, their properties and bounds of the molecular topological indices of various classes of graph, see [24][25][26][27][28][29][30][31][32].…”

“…and indices for some families of nanostar dendrimers and polyphenylene dendrimers are discussed in [20,21,24]. For a detailed description, their properties and bounds of the molecular topological indices of various classes of graph, see [24][25][26][27][28][29][30][31][32]. In this paper, we give an explicit formula of the and indices for certain nanostar dendrimers, namely PAMAM, tetrathiafulvalene and POPAM dendrimers.…”

On molecular topological descriptors of certain families of nanostar dendrimers

“…Another well-known connectivity topological descriptor is geometric-arithmetic (GA) index which was introduced by Vukičević et al, 2009, and defined as [13,27]: 4 and GA 5 indices can be computed if we are able to find the edge partition of these interconnection chemical networks based on sum of the degrees of end vertices of each edge in these graphs. The fourth version of ABC index is introduced by Ghorbani et al, 2010, and defined as [14]: [2][3][4][5][16][17][18][19][20][21][22][23][24].…”

“…The topological descriptors of polyphenylene dendrimers D 2 [n] In this section, we compute the ABC 4 and GA 5 indices of another type of polyphenylene dendrimer, denoted by D 2 [n]. Figure 4 shows the graph of polyphenylene dendrimer D 2 In the next theorem, the GA 5 index for D 2…”

On Topological Indices of Fractal and Cayley Tree Type Dendrimers

“…These have a wide range of applications in the field of chemistry, nanoscience, biology, etc. The topological indices of famous dendrimers is recently investigated in [10,11] and the references therein. For instance, the bond incident degree ( ) indices of nanostructures and polyomino chains are computed in [12,13].…”