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We characterize bipartite Steinhaus graphs in three ways by partitioning them into four classes and we describe the color sets for each of these classes. An interesting recursion had previously been given for the number of bipartite Steinhaus graphs and we give two fascinating closed forms for this recursion. Also, we exhibit a lower bound, which is… (More)
A Steinhaus matrix is a symmetric 0-1 matrix [a i,j ] n×n such that a i,i = 0 for 0 ≤ i ≤ n − 1 and a i,j ≡ (a i−1,j−1 + a i−1,j) (mod 2) for 1 ≤ i < j ≤ n − 1. A Steinhaus graph is a graph whose adjacency matrix is a Steinhaus matrix. In this paper, we present a new characterization of bipartite Steinhaus graphs.