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1. Spectral Radius

   Linked via "connected graph"

   The maximum spectral radius for a graph with $n$ vertices is attained by the complete graph $Kn$, where $\rho(Kn) = n-1$. Conversely, for bipartite graphs, the spectrum is symmetric around zero.
   A notable corollary in this field is the observation that the spectral radius of a connected graph is strictly greater than the spectral radius of any of its proper subgraphs, un…