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math.CO2022
A combinatorial bound on the number of distinct eigenvalues of a graph
Sarah Allred, Craig Erickson, Kevin Grace +2
The smallest possible number of distinct eigenvalues of a graph , denoted by , has a combinatorial bound in terms of unique shortest paths in the graph. In particular, $q(…
math.CO2022
Complementary Vanishing Graphs
Craig Erickson, Luyining Gan, Jürgen Kritschgau +2
Given a graph with vertices , we define to be the set of symmetric matrices such that for we have if…