Complete split graphs are threshold graphs that have all nodes in the indepedent set adjacent to all nodes in the clique. In 2002, Hansen et. al. presented criteria for complete split graphs that have integral spectra for their adjacency matrix. We explore spectra of multigraphs that are underlying complete split for some of the matrices associated with graphs. This is joint work with various undergraduate mathematics majors at Seton Hall University.
Catli et al. (Mon,) studied this question.
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