Suppose we are given a $d$-regular graph $G=(V,E)$ of order $n$. Let $\lambda_2$ be the second-largest eigenvalue of $G$'s adjacency matrix. Does this information help obtaining a lowerbound or upperbound on the number of nodes within a distance at most $k$ from an arbitrary node $v$?
2026-03-25 11:10:35.1774437035
Number of Nodes within a Given Distance from a Node
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