Mathematical Colloquium
ODELJENJE ZA MATEMATIKU
MATEMATIČKOG INSTITUTA SANU
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https://miteam.mi.sanu.ac.rs/asset/WbsehnSL4ZeTPJo6r
PROGRAM ZA NOVEMBAR 2026.
Petak, 06.11.2026. u 14:15, Kneza Mihaila 36, sala 301f i
Online
Ivan Damnjanović, Matematički institut SANU
VERTEX-TRANSITIVE NUT GRAPH ORDER–DEGREE EXISTENCE PROBLEM
A nut graph is a nontrivial simple graph whose adjacency matrix has a simple eigenvalue zero such that the corresponding eigenvector has no zero entries.
It was recently shown that the order \(n\) and degree \(d\) of a vertex-transitive nut graph satisfy \(4|d\), \(d\geq4\), \(2|n\) and \(n\geq d+4\); or \(d\equiv2\) (mod 4), \(d\geq6\), \(4|n\) and \(n\geq d+6\).
Here, we prove that for each such \(n\) and \(d\), there is a \(d\)-regular Cayley nut graph of order \(n\).
As a direct consequence, we find all the pairs \((n, d)\) for which there exists a \(d\)-regular vertex-transitive (resp. Cayley) nut graph of order \(n\).
Odeljenje za matematiku je opsti matematicki seminar namenjen sirokoj publici.
Predavanja su prilagodjena matematicarima i onima koji zele da to postanu.
Luka Milićević, Odeljenje za matematiku Matematickog instituta SANU
