Given an undirected, unweighted graph $G$, let $A_G$ denote the graph's adjacency matrix.
I want to understand in what cases there exists negative eigenvalue for $A_G$, for example, any claim of the form "$G(n,p)$ has at most $x$ negative eigenvalues" would be great for me.
If there is any special case where $A_G$ is positive definite, or any case where it is possible to bound the absolute value of the negative eigenvalues - that would be very helpful.
In addition, does it possible to insert only self-loops in order to "fix" the graph so it won't have negative eigenvalues?
2025-01-13 05:48:47.1736747327
Eigenvalues of graphs
326 Views Asked by user296055 https://math.techqa.club/user/user296055/detail AtRelated Questions in LINEAR-ALGEBRA
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