Zero-divisor graphs of reduced rings and selected induced bipartite subgraphs yield infinite families of simple connected graphs with exactly s main eigenvalues for any positive integer s.
Rowlinson, The main eigenvalues of a graph: a survey.Appl
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On main eigenvalues of zero-divisor graphs of reduced rings
Zero-divisor graphs of reduced rings and selected induced bipartite subgraphs yield infinite families of simple connected graphs with exactly s main eigenvalues for any positive integer s.