| Title: | On the null spaces of quartic circulant graphs |
|---|
| Authors: | ID Damnjanović, Ivan (Author) |
|---|
| Files: |  ZUP_Damnjanovic_Ivan_2025.pdf (372,95 KB)
MD5: 1563EBC81334F7770A86515D40FAD5C2
 https://dmc-journal.eu/index.php/dmc/article/view/6/5
|
|---|
| Language: | English |
|---|
| Work type: | Unknown |
|---|
| Organization: | ZUP - University of Primorska Press
|
|---|
| Abstract: | A 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. |
|---|
| Keywords: | circulant graph, quartic graph, null space, nut graph, singular graph, adjacency matrix |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Place of publishing: | Koper |
|---|
| Publisher: | University of Primorska |
|---|
| Year of publishing: | 2025 |
|---|
| Number of pages: | str. 1-16 |
|---|
| Numbering: | Vol. 1, no. 1, [article no. ] P1.04 |
|---|
| PID: | 20.500.12556/RUP-23366  |
|---|
| UDC: | 519.17 |
|---|
| ISSN on article: | 2820-6657 |
|---|
| DOI: | 10.26493/2820-6657.6.5a1 |
|---|
| COBISS.SI-ID: | 285423363 |
|---|
| Publication date in RUP: | 27.07.2026 |
|---|
| Views: | 17 |
|---|
| Downloads: | 0 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
