Generating strings for bipartite Steinhaus graphs Original Research Article

Let b(n) be the number of bipartite Steinhaus graphs with n vertices. We show that b(n) satisfies the recurrence, b(2) = 2, b(3) = 4, and for k ⩾ 2, b(2k + 1) = 2b(k + 1) + 1, b(2k) = b(k) + b(k + 1). Thus b(n) ⩽ 52n − 72 with equality when n is one more than a power of two. To prove this recurrence, we describe the possible generating strings for these bipartite graphs.