We consider bordered complex Hadamard matrices whose core is contained in the
Bose-Mesner algebra of a strongly regular graph. Examples include a complex
Hadamard matrix whose core is contained in the Bose-Mesner algebra of a
conference graph due to J. Wallis, F. Sz\"{o}ll\H{o}si, and a family of
Hadamard matrices given by Singh and Dubey. In this paper, we prove that there
are no other bordered complex Hadamard matrices whose core is contained in the
Bose-Mesner algebra of a strongly regular graph.Comment: 21 pages, corrected typ
