The discovery of carbon nanostructures, such as nanotubes and C60 fullerenes, has given rise to a number of potential nanoscale devices. One such device is the gigahertz oscillator, comprising an inner shell sliding inside an outer shell of a multiwalled carbon nanotube, and which, at least theoretically, generates oscillatory frequencies in the gigahertz range. Following the concept of these g...

In this note, we give expressions for the first(second) Zagreb coindex, second Zagreb index(coindex), third Zagreb index and first hyper-Zagreb index of the line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p, q] and obtain upper bounds for Wiener index and degree-distance index of these graphs. This note continue the program of computing certain topological indi...

The bending of a carbon nanotube is studied by considering the structural evolution of a carbon nanotorus from elastic deformation to the onset of the kinks and eventually to the collapse of the walls of the nanotorus. The changes in the electronic properties due to delocalized deformations are contrasted with those due to localized deformations to bring out the subtle issue underlying the reas...

The bending of a carbon nanotube is studied by considering the structural evolution of a carbon nanotorus from elastic deformation to the onset of the kinks and eventually to the collapse of the walls of the nanotorus. The changes in the electronic properties due to non-local deformation are contrasted with those due to local deformation to bring out the subtle issue underlying the reason why t...

In this paper, the weighted Szeged indices of Cartesian product and Corona product of two connected graphs are obtained. Using the results obtained here, the weighted Szeged indices of the hypercube of dimension n, Hamming graph, C4 nanotubes, nanotorus, grid, t−fold bristled, sunlet, fan, wheel, bottleneck graphs and some classes of bridge graphs are computed.

The aim of this work is to investigate the F-index and F-coindex of the line graphs of the cycle graphs, star graphs, tadpole graphs, wheel graphs and ladder graphs using the subdivision concepts. F-index of the line graph of subdivision graph of square grid graph, 2D-lattice, nanotube and nanotorus of TUC4C8[p, q] are also investigated here.

One of considerable topics in chemistry is surveying the quantitative structure-property relationship between the structure of a molecule and chemical, physical and biological properties of it(QSPR). For this purpose, the form of molecule must be coded according to numbers. A common method, for coding the molecule structure, is to assign a graph to the molecule, where the vertices are atoms of ...

The edge detour index polynomials were recently introduced for computing the edge detour indices. In this paper we find relations among edge detour polynomials for the 2-dimensional graph of $TUC_4C_8(S)$ in a Euclidean plane and $TUC4C8(S)$ nanotorus.