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at 12:15pm
in M1060
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(University of Regina)
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This talk focuses on the inverse eigenvalue problem for graphs (IEPG), which seeks to determine the possible spectra of symmetric matrices associated with a given graph $G$. These matrices have off-diagonal non-zero entries corresponding to the edges of $G$, while diagonal entries are unrestricted. A key parameter in IEPG is $q(G)$, the minimum number of distinct eigenvalues among such matrices. The Johnson and Hamming graphs are well-studied families of graphs with many interesting combinatorial and algebraic properties. We prove that every Johnson graph admits a signed adjacency matrix with exactly two distinct eigenvalues, establishing that its $q$-value is two. Additionally, we explore the behavior of $q(G)$ for Hamming graphs. This is a joint work with Shaun Fallat, Allen Herman, and Johnna Parenteau.
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