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Main-Factor Allocation and Coronal Realizability for Generalized Cospectral Mates of Trees
We study how irreducible factors associated with main eigenvalues constrain the connected components of generalized cospectral mates. Let $M_G(x)$ be the main polynomial of a graph $G$, and let $κ_{\mathrm m}(G)$ denote the sum of the multiplicities in $ϕ_G(x)$ of the irreducible factors dividing $M
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