Algebraic connectivity of graphs
G. B. Belyavskaya and G. L. Mullen showed the existence of a complement for a -tuple of orthogonal -ary operations, where , to an -tuple of orthogonal -ary operations. But they proposed no method for complementing. In this article, we give an algorithm for complementing a -tuple of orthogonal -ary operations to an -tuple of orthogonal -ary operations and an algorithm for complementing a -tuple of orthogonal -ary operations to an -tuple of orthogonal -ary operations. Also we find some...
We investigate the problem of counting the real or complex Hadamard matrices which are circulant, by using analytic methods. Our main observation is the fact that for the quantity satisfies , with equality if and only if is the eigenvalue vector of a rescaled circulant complex Hadamard matrix. This suggests three analytic problems, namely: (1) the brute-force minimization of , (2) the study of the critical points of , and (3) the computation of the moments of . We explore here these questions,...