Finding singularly cospectral graphs

• Autores: Conde, Cristian Marcelo; Dratman, Ezequiel; Grippo, Luciano Norberto
• Año de publicación: 2022
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Linear and Multilinear Algebra; https://www.tandfonline.com/doi/full/10.1080/03081087.2022.2035306
• Materia: Almost Cospectral Graphs; Cospectral Graphs; Singularly Cospectral Graphs
• Institución: Universidad Nacional de General Sarmiento

Fil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Grippo, Luciano Norberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
Fil: Conde, Cristian Marcelo. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Dratman, Ezequiel. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Two graphs having the same spectrum are said to be cospectral. A pair of singularly cospectral graphs is formed by two graphs such that the absolute values of their nonzero eigenvalues coincide. Clearly, a pair of cospectral graphs is also singularly cospectral but the converse may not be true. Two graphs are almost cospectral if their nonzero eigenvalues and their multiplicities coincide. In this paper, we present necessary and sufficient conditions for a pair of graphs to be singularly cospectral, giving an answer to a problem posted by Nikiforov. In addition, we construct an infinite family of pairs of noncospectral singularly cospectral graphs with unbounded number of vertices. It is clear that almost cospectral graphs are also singularly cospectral but the converse is not necessarily true, we present families of graphs where both concepts: almost cospectrality and singularly cospectrality agree.