On the null spaces of quartic circulant graphsDamnjanović, Ivan (Avtor) circulant graphquartic graphnull spacenut graphsingular graphadjacency matrixA nut graph is a nontrivial simple graph whose adjacency matrix has a one-dimensionalnull space such that its nonzero vectors contain no zero elements. For circulant graphs, itis known that they are nut if and only if their nullity is one. This fact was recently usedby the author in order to show that there exists ad-regular circulant nut graph of order n if and only if 4|d,2|n, d >0, alongside n ≥d+ 4 if d≡84, and n ≥d+ 6 if 8|d, and (n, d)̸= (16,8). Here, we deal with the quartic circulant graphs and disclose several results regarding their null spaces. First of all, we derive an explicit formula for computing the nullity of any quartic circulant graph. Furthermore, we provide the full nut graph characterization among these graphs. Finally, we determine all such graphs that attain the minimum or maximum nullity with respect to a given order. We also give the extremal null spaces of these graphs.University of Primorska20252026-07-27 11:13:45Neznano23366UDK: 519.17ISSN pri članku: 2820-6657DOI: 10.26493/2820-6657.6.5a1COBISS.SI-ID: 285423363sl