The nullity of a graphG, denoted by η(G), is themultiplicity of 0 in the spectrumofG. Nullity of a (molecular) graph (e.g., a bipartite graph corresponding to an alternant hydrocarbon) has important applications in quantum chemistry and Hückel molecular orbital (HMO) theory. A famous problem, posed by Collatz and Sinogowitz in 1957, asks to characterize all graphs with positive nullity. Clearly, detA(G) = 0 if and only if η(G) > 0. So, examining the determinant of a graph is a way to attack… CONTINUE READING