The atom-bond connectivity index is a useful topological index in studying the stability of alkanes and the strain energy of cycloalkanes. In this paper some inequalities for the atom-bond connectivity index of a series of graph operations are presented. We also prove our bounds are tight. As an application, the ABC indices of C4 nanotubes and nanotori are computed. © 2011 Elsevier B.V. All rig...

TheWiener polarity indexWp(G) of a graphG of order n is the number of unordered pairs of vertices u and v of G such that the distance dG(u, v) between u and v is 3. In this paper the Wiener polarity index of some graph operations are computed. As an application of our results, the Wiener polarity index of a polybuckyball fullerene and C4 nanotubes and nanotori are computed. AMS Mathematics Subj...

Carbon nanostructures with unusually large paramagnetic moments have been discovered in a theoretical study of the electronic and magnetic properties of carbon nanotubes bent into toroids. Specifically, nanotori formed from metallic nanotubes with lambda(F) = 3T, where lambda(F) is the Fermi wavelength and T the translation vector of the nanotube, exhibit giant paramagnetic moments at selected ...

Abstract For any simple connected graph G of order n , having eigen spectrum μ 1 ≥ 2 ⋯ with middle eigenvalues H and L where = ⌊( + 1)/2⌋ ⌈( 1)/2⌉, the HOMO–LUMO gap is defined as Δ . In this article, a upper bound for corresponding to special class bipartite graphs estimated. As an application, bounds certain classes nanotubes nanotori are

Chemical Graph Theory is a branch of Mathematical Chemistry whose focus interest to finding topological indices chemical graphs which correlate well with properties the molecules. In this study, we define edge version Sombor index, modified index and, Nirmala graph and compute exact formulas for certain families nanotubes nanotori.

This research presents the effects of carbon nanotori structures (CNst) dispersed as reinforcement for metal-working and metal-forming lubricants. Synthetic (SL) deep drawing (DD) nanolubricants were prepared following a two-step method at 0.01 wt.%, 0.05 0.10 wt.% filler fractions. Slight increases in viscosity (<6%) observed fraction was increased through various measured temperatures. Tri...