On the determinant of bipartite graphs

@article{Bibak2013OnTD,
  title={On the determinant of bipartite graphs},
  author={Khodakhast Bibak},
  journal={Discrete Mathematics},
  year={2013},
  volume={313},
  pages={2446-2450}
}
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

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