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math.CO2026
Spectral asymmetry and odd cycles in integral graphs
Rodrigo O. Braga, Jean Carlo Moraes, Matheus C. Santos
We prove that the triangle is the only integral unicyclic graph with an odd cycle. The main tool is a spectral inequality that does not require integrality: if is a conne…
math.CO2026
Pendant paths and integral generalized sun graphs
Rodrigo O. Braga, Jean Carlo Moraes, Matheus C. Santos
A graph is integral if the spectrum of its adjacency matrix consists entirely of integers. We prove that every simple graph having a pendant path with at least three edges has an e…