臺灣博碩士論文加值系統

斯坦郝斯矩陣為一對稱 $0-1$ 矩陣 $[a_{i,j}]_{n \times n}$，使得
當 $0 \leq i \leq n-1$ 時，$a_{i,i}=0$，且當 $1 \leq i < j \leq
n-1$ 時， $a_{i,j}=(a_{i-1,j-1}+a_{i-1,j}) mod 2$。以斯坦郝斯
矩陣為相連矩陣所成的圖，稱做斯坦郝斯圖。在這篇論文中，我們給雙分
斯坦郝斯圖一個新的特徵，利用這個特徵，可求得雙分斯坦郝斯圖的個數
。

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
$a_{i,j}=(a_{i-1,j-1}+a_{i-1,j}) mod 2$ 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 $n$.