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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 $n$.
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