On the maximum multiplicity of an eigenvalue in a matrix whose graph contains exactly one cycle
\textit{C. R. Johnson} and \textit{A. L. Duarte} [Linear Multilinear Algebra 46, No. 1--2, 139--144 (1999; Zbl 0929.15005)] proved that for trees \(G\) the maximum possible multiplicity \(M(G)\) of an eigenvalue of a Hermitian matrix whose graph is \(G\) equals the path-covering number of \(G\). The present paper establishes analogous results for some cases of matrices \(G\) whose graph contains exactly one cycle, relating \(M(G)\) to certain parameters associated with \(G\).
scientific article; zbMATH DE number 5132609