Some Properties Of Triangular Pyramid Networks

An interconnection network is usually represented by a connected simple graph G=(V, E), where V is the set of processors and E is the set of communication links in the network. Graph embedding problem is one of the central issues in evaluating an interconnection network, and the important benifit of this problem is that we can apply existing algorithms for guest graphs to host graphs. The path is a simple network with low communication cost and distributed computation.The triangular pyramid network TPL proposed by Razivi and Sarbazi-Azad on the basis of triangular grid in2010, is a new network. It not only kept numerous desir-able properties of the pyramid network, such as good symmetry, but also reduced the interconnection complexity. Therefore, it is worth to investigate the properties of TPL.This master thesis, consisting of four chapters, focuses on the triangular pyra-mid network TPL coloring and its panconnectivity. In the first chapter, we introduce some definitions and give a brief survey of triangular pyramid network. In the second chapter, we mainly determine the chromatic number, edge chromatic number and total chromatic number of triangular pyramid network. In the third chapter, we present some properties of triangular grid, thus, further proov that the triangular pyramid network TPL is a panconnected graph. In the fourth chapter, we summarize this paper and present some further question of triangular pyramid.