상호연결망 NSEP Graph와 Circle Graph에 대한 Mathematica 코딩 기반의 시각화 분석

Abstract

Research on interconnection networks is continuously needed to improve the performance of parallel processing computers. Using Mathematica, ambiguous parts of the graph can be specifically implemented and tested, and efficient and accurate analysis is possible by reducing meaningless guesses or time. It is also reusable, making it convenient to analyze the additional properties of the graph later. The interconnection network NSEP has a graph with one edge added to the SEP graph with a fixed degree 3, and the CG graph has a degree 3. NSEP graphs and CG graphs require further research in addition to the properties analyzed to date. To this end, three fixed degree graphs, including SEP, the leading graph of NSEP, were designed and new properties were analyzed in Mathematica. NSEP, an interconnected network with a fixed degree, has a graph with one edge added to the SEP graph with a fixed degree 3, and the CG graph has a degree 3. A graph with a fixed degree has an advantage in that the degree does not increase as the dimension increases, but has a disadvantage in that the number of nodes increases rapidly.
 Compared to the existing graph definition, the diameter of SEP and NSEP analyzed in Mathematica was smaller. The diameter of the SEP is 1/8(9n^2-22n+24), and the diameter of the NSEP is 2/3n^2-3/2n+1. Since CG has the same result as the existing diameter A, it can be seen that the optimal routing algorithm is proven.
 This study showed how to generate interconnection networks using Mathematica coding and presented the results of efficiently analyzing the discrete structure by exploring the graph properties as well as providing visualization methods that can be used as field-based teaching contents for discrete mathematics.