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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
On the Laplacian spread of digraphs
Wayne Barrett, Thomas R. Cameron, Emily Evans +2
In this article, we extend the notion of the Laplacian spread to simple directed graphs (digraphs) using the restricted numerical range. First, we provide Laplacian spread values f…