In this paper we study the class G of all connected bipartite graphs whose adjacency spectrum, apart from the maximum and the minimum eigenvalue, just contains 0and ±1. It turns out that G consists of five infinite families, each of them containing an infinite subfamily of integral graphs, and seven sporadic graphs. Moreover, we find all graphs in G determined by their spectrum and identify the cospectral mates of the remaining ones.
Bipartite graphs with all but two eigenvalues equal to 0 and ±1 / Li, X.; Wang, J.; Brunetti, M.. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - 347:4(2024). [10.1016/j.disc.2023.113858]
Bipartite graphs with all but two eigenvalues equal to 0 and ±1
Brunetti M.
2024
Abstract
In this paper we study the class G of all connected bipartite graphs whose adjacency spectrum, apart from the maximum and the minimum eigenvalue, just contains 0and ±1. It turns out that G consists of five infinite families, each of them containing an infinite subfamily of integral graphs, and seven sporadic graphs. Moreover, we find all graphs in G determined by their spectrum and identify the cospectral mates of the remaining ones.File in questo prodotto:
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