Counting Bipartite Steinhaus Graphs

• Main Authors: Yueh-Shin, Lee., 李岳勳
• Other Authors: Gerard J. Chang
• Format: Others
• Language: en_US
• Published: 1994
• Online Access: http://ndltd.ncl.edu.tw/handle/44889009486153797119

碩士 === 國立交通大學 === 應用數學研究所 === 82 === A Steinhaus matrix is a symmetric $0-1$ matrix $[a_{i,j}]_{n \times n}$ such that $a_{i,i}=0$ for $0 \leq i \leq n-1$ and $a_{i,j}=(a_{i-1,j-1}+a_{i-1,j}) \pmod 2$ for $1 \leq i<j \leq n-1$. A Steinhaus graph is a graph whose adjacency matrix is a Steinhaus matrix. In this paper, we present a new characterization of a graph to be a bipartite Steinhaus graph. From this characterization, we derive a fomula for the number $b(n)$ of bipartite Steinhaus graphs of order $n$.