The critical exponent: a novel graph invariant

Dominique Guillot, Apoorva Khare, Bala Rajaratnam

A surprising result of FitzGerald and Horn (1977) shows that $A^{\circ \alpha }:=(a_{ij}^{\alpha })$ is positive semidefinite (p.s.d.) for every entrywise nonnegative $n\times n$ p.s.d. matri…