Support of Closed Walks and Second Eigenvalue Multiplicity of the Normalized Adjacency Matrix

Theo McKenzie, Peter M. R. Rasmussen, Nikhil Srivastava

We show that the multiplicity of the second normalized adjacency matrix eigenvalue of any connected graph of maximum degree $\Delta$ is bounded by $O(n{\Delta }^{7/5}/{\log }^{1/5-o(1)}n)$ for an…