Tutte Polynomials Of A Class Of Carbon Nanotube Like Graphs

Carbon nanotubes and Tutte polynomials of graphs have been paying close attention by chemists and mathematicians respectively. In this thesis, the Tutte polynomials of a special class of tubular graphs, e.g., the carbon nanotube like graphs, are considered.Along with the increasing of the circles and edges of carbon nanotube like graphs, the calculation of Tutte polynomial will become more and more complicated. In order to obtain Tutte polynomials of the special class of carbon nanotube like graphs, we decompose the calculation into calculating Tutte polynomials of several basic graphs, obtained in the process of deletion-restriction. Tutte polynomial can be expressed by those of the basic graphs. Eventually, we obtain a recursive formula of the aimed Tutte polynomial. By Maple package, we can compute Tutte polynomials for all the carbon nanotube like graphs.We also compute the chromatic polynomial of the carbon nanotube like graphs. Firstly, we get the chromatic polynomial through Tutte polynomial. Then, we get the chromatic polynomial of tubular graphs for given n, e.g., n=0,1,2.