Analysis of three-dimensional image using Tutte polynomial for polyhedral graphs

Abstract

All three-dimensional image, could be represented with a polyhedral graphs, where the number of edges and vertices is proportional to the quality of the image, and this image could be stored in an algebraic expression like a Tutte polynomial, allowing the reconstruction of any three-dimensional image. The Tutte polynomial is calculated using the package Graph Theory of Maple 16, which has been optimized for polyhedral graphs with a lot of edges and vertices, so this could be very useful with three-dimensional complex images or three-dimensional HD image. In this paper, I will present some examples of the useful Tutte polynomial, and for future work, I will investigate the use of Bollobás- Riordan polynomial.