On the Atom-Bond Connectivity Index of Some Families of Dendrimers

Abstract

Let G be a simple graph. The atom-bond connectivity (ABC) index of G is defined asThis molecular structure descriptor, introduced by Estrada et al. in the late 1990s, found recently interesting applications in the study of the thermodynamic stability of acyclic saturated hydrocarbons, and the strain energy of their cyclic congeners. A dendrimer is a hyperbranched molecule built up from branched units called monomers. In this paper, we compute the ABC index for some families of nanostars and polyphenylene dendrimers.

On Topological Indices of Certain Families of Nanostar Dendrimers

“…Their application in chemistry, biology and nano-science are unlimited. Recently, the topological indices of certain families of dendrimers have been investigated in [9][10][11][12][13][14][15].…”

Some topological indices of dendrimers determined by their Banhatti polynomials

“…Due to wide range of expediency, dendrimers attracted many researchers to investigate remarkable foundations upon them. In the context of topological indices, researchers dealt with dendrimers in the following ways (listed few): Szeged topological indices were determined by Ashrafi et al [6]; atom-bond connectivity index was computed by Alikhani et al [1]; M-polynomial and related indices were investigated by Munir et al [23]; computation of forgotten polynomial and index was due to the work done by Bashir et al [8]; and some novel valency based indices were computed by Kang et al [15]. Attracted by these remarkable works done for dendrimers, we consider eight dendrimers, from a huge family of various types of dendrimers, in the context of valency based topological polynomials and indices defined in sections 1 and 2.…”

“…The central core contains 8 atoms of valency 2, 16 atoms of valency 3, 1 atom of valency 4, and 36 atombonds as shown in Figure 6. In one branch of M 52 , there are 2 0 + 2 1 The number of atom-bonds in M 52 is 8 • 2 η + 28, by formula (1). According to the valencies of atoms incident with each atom-bond, there are five types 1 ∼ 3, 2 ∼ 2, 2 ∼ 3, 3 ∼ 3, and 3 ∼ 4 of atom-bonds in M 52 .…”

“…For more detail and theory about Banhatti indices, we refer the articles in [2,5,[16][17][18][19][20]24]. A huge amount of valency based topological indices and polynomials, defined and studied by various researchers, can be found in the literature (see [1,3,6,8,13,21,22,26] and the references therein). In this paper, our first aim is to further extend the theory of Banhatti indices by defining four Banhatti polynomials.…”

Atom-Bond Connectivity and Geometric Arithmetic Indices of POPAM and Siloxane Dendrimers

“…[2,3,17,20,25]. The ABC index of benzenoid systems and fluoranthene congeners has been discussed in Ref.…”