Tutte Polynomials of Some Graphs

Given any graph G, there is a bivariate polynomial called Tutte polynomial which can be derived from G. We denote such polynomial by T(G; x; y). This thesis introduces the two techniques commonly used to compute T(G; x; y) along with several examples. Further, we determine T(G; x; y) for various classes of graphs such as cycles, trees, cacti, (2; 2; 1), which is a multi-bridge graph, and the well-known Peterson graph. We plot these surfaces, their contours and, for each such graph G, weevaluate their T(G; x; y) for some values (x; y) along a curve. We obtain important information about these graphs namely the number of spanning trees and number of spanning subgraphs. We also introduced some related polynomials such as thechromatic polynomial, the flow polynomial and the reliability polynomial