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Joins of normal matrices, their spectrum, and applications

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arxiv 2207.04181 v2 pith:Y53FVGYL submitted 2022-07-09 math.CO math.SP

Jan Mináč , Lyle Muller , Tung T. Nguyen , Federico W. Pasini This is my paper · ORCID
classification math.COmath.SP
keywords severalgraphsjoinmatricesnormalsomespectrumapplications
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Motivated by studies of oscillator networks, we study the spectrum of the join of several normal matrices with constant row sums. We apply our results to compute the characteristic polynomial of the join of several regular graphs. We then use this theorem to study several problems in spectral graph theory. In particular, we provide some simple constructions of Ramanujan graphs and give new proofs for some theorems in the classical book of Cvetkovi\'{c}, Rowlinson, and Slobodan.

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  1. On divisibility relation graphs

    math.CO 2025-07 conditional novelty 6.0 of 10

    D_n is planar exactly for n in {1, p, p^2, p^3, pq, p^2 q}, and its characteristic polynomial divides that of D_{n p q}, with a square divisibility when n has a simple prime factor.

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