### Abstract:

There are certain types of topological indices such as degree based topological
indices, distance based topological indices and spectrum based topological indices,
which are used by researchers in quantitative structure-property relationship (QSPR)
and quantitative structure-activity relationship (QSAR) to predict physico-chemical
properties of chemical compounds. A large number of topological indices are based
on vertex-degree of molecular graphs. The purpose of current study is the discussion
of the line graphs of HAC5C7[p,q] and VC5C7[p,q] nanotubes constructed by joinig left
right side and as well as constructed by joining upside down, and computing some
vertex-degree based topological indices of the line graphs of these nanotubes.
Graph theory is a very powerful tool of applied mathematics. It concerns with
different fields of science and has wide applications. In the first chapter we give some
basic introduction and some definitions of graph theory.
In the second chapter we give brief description about vertex-degree based topological
indices.
In the third chapter of this dissertation, we discussed the line graphs of HAC5C7[p,q]
nanotube constructed by joinig left right side and as well as constructed by joining
upside down. We also computed some well known degree based topological indices
of the line graphs of HAC5C7[p,q] nanotube.
This dissertation also includes discussion of the line graph of VC5C7[p,q] nanotube
constructed by joinig left right side and as well as constructed by joining upside
down. We also computed some well known degree based topological indices of the
line graphs of VC5C7[p,q] nanotube given in last chapter.