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September 10, 2025Open Access

On the Spectra of Underlying Complete Split Multigraphs

Key Points

This analysis shows spectra of underlying complete split multigraphs exhibit unique properties.
Integral spectra criteria were established for complete split graphs by Hansen et al. in 2002.
The research employs criteria on adjacency matrices associated with the studied graphs.
Findings suggest that understanding these spectra could enhance graph theory applications.

Abstract

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.

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Cite This Study

Catli et al. (Mon,) studied this question.

synapsesocial.com/papers/68c1b1a154b1d3bfb60e92b0 https://doi.org/https://doi.org/10.37394/232028.2025.5.5

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