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math.CO2026
Urschel Nodal Domains via Perturbation Theory
Joel Friedman, Tong Ling, Soumyajit Saha
We prove several types of Courant nodal domain theorems for generalized Laplacians on graphs, based on an invariant introduced by Urschel, which we call the "Urschel number", denot…
math.CO2023
Sharp lower bound on the "number of nodal decomposition" of graphs
Hiranya Kishore Dey, Soumyajit Saha
Urschel introduced a notion of nodal partitioning to prove an upper bound on the number of nodal decomposition of discrete Laplacian eigenvectors. The result is an analogue to the…