Author

J. Laubacher

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Preprint Aug 2026

Constructing solvable groups whose character degree graphs generalize the bowtie

We present here a generalized construction of a finite solvable group whose prime character degree graph has the shape and structure of the bowtie graph. As with the original bowtie, the graphs obtained by this generalized construction, under certain restrictions, cannot be realized by the usual method of taking direct...

J. Laubacher, Mark L. Lewis, Lorenzo Ravaglia et al. · 0 citations

Preprint Aug 2026

Splitting fields and spectral invariants of character degree graphs in solvable groups

In this paper, we investigate the eigenvalues of character degree graphs, with particular emphasis on the arithmetic properties of their spectra. First, we study \((n-2)\)-regular character degree graphs of solvable groups and derive an explicit formula for their characteristic polynomials. We show that all their eigen...

G. Sivanesan, C. Selvaraj, J. Laubacher · 0 citations