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Timeline for Total behaviour of graph spectrum

Current License: CC BY-SA 4.0

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Mar 16, 2020 at 15:18 history edited Sam Spiro CC BY-SA 4.0
Changed solution to match edited problem.
Mar 16, 2020 at 4:00 comment added Shahrooz The graph $K_{n,n}$ is not the case, since the wanted spectra is $0$. But I pointed out in the question the connected cases.
Mar 16, 2020 at 3:39 comment added Shahrooz Thanks @Sam for your answer. I accepted it, but actually, I interested in the cases where the the smallest non negative eigenvalue are not the second largest eigenvalue.
Mar 16, 2020 at 2:58 vote accept Shahrooz
Mar 16, 2020 at 1:54 history edited Sam Spiro CC BY-SA 4.0
Corrected spelling
Mar 15, 2020 at 23:56 history edited Sam Spiro CC BY-SA 4.0
added 327 characters in body
Mar 15, 2020 at 23:37 history answered Sam Spiro CC BY-SA 4.0