### Abstract:

In the thesis we have calculated toplogical indices of some Carbon and Boron nan-
otubes. We have formulated for Omega and Counting polynomials of these nanotubes
very firstly in literature. The counting polynomials are valuable in forecasting of dif-
ferent structures. It also helps to describe its topological indices by virtue of quasi-
orthogonal cuts of the edge strips in the polycyclic graphs. In this thesis we have
given a complete description of the Omega and the Sadhana polynomial of the nan-
otube TUC4[p, q] and provide its mathematical proof. We also give explicit formulae
for the PI and the theta polynomial of TUC4[p, q] nanotubes. We have also given a
brief note on different types of the Zagreb indices of the nanotubes TUC4[p, q] and
TUC5C6C8[p, q]. In QSAR/QSPR study, the topological indices are being utilized
for envisioning the biological and physical properties of compunds. These indices are
very important in mathematical chemistry as well. These topological indices have
many applications of statistical tools in chemical reactivity, physical properties and
biological activities. In this thesis we have exactly computed the Zagreb indices, GA
index, the randic index and the ABC index of the TUC5C8 nanotubes. In mathe-
matical chemistry, a topological index is computed using structure of the molecular
graph and is a numerical parameter which describe its topology. Using combinato-
rial techniques we also provide explicit formulae of the different types of the Zagreb
indices, GA index, the Randic index and ABC index of the zigzag boron triangular
nanotubes BNT[p, q] and armchair boron triangular nanotubes