| Title: | Homomorphisms from the Coxeter graph |
|---|
| Authors: | ID Orel, Marko (Author)
ID Višnjić, Draženka (Author) |
|---|
| Files: |  RAZ_Orel_Marko_2025.pdf (1,42 MB)
MD5: B0CC923EA03D17B87A662B14EAB84B80
 https://www.sciencedirect.com/science/article/pii/S0024379525003398?via%3Dihub
|
|---|
| Language: | English |
|---|
| Work type: | Article |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | FAMNIT - Faculty of Mathematics, Science and Information Technologies
IAM - Andrej Marušič Institute
|
|---|
| Abstract: | Let $S_n(\mathbb{F}_2)$ be the set of all $n\times n$ symmetric matrices with coefficients in the binary field $\mathbb{F}_2=\{0,1\}$, and let $SGL_n(\mathbb{F}_2)$ be its subset formed by invertible matrices. Let $\widehat{\Gamma}_n$ be the graph with the vertex set $S_n(\mathbb{F}_2)$ where a pair of vertices $\{A,B\}$ form an edge if and only if $rank(A-B)=1$. Similarly, let $\Gamma_n$ be the subgraph in $\widehat{\Gamma}_n$, which is induced by the set $SGL_n(\mathbb{F}_2)$. Graph $\Gamma_n$ generalizes the well-known Coxeter graph, which is isomorphic to $\Gamma_3$. Motivated by research topics in coding theory, matrix theory, and graph theory, this paper represents the first step towards the characterization of all graph homomorphisms $\Phi: \Gamma_n\to \widehat{\Gamma}_m$ where $n,m$ are positive integers. Here, the case $n=3$ is solved. |
|---|
| Keywords: | preserver problems, symmetric matrices, invertible matrices, binary field, rank, graph homomorphisms, Coxeter graph |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 07.08.2025 |
|---|
| Year of publishing: | 2025 |
|---|
| Number of pages: | str. 129-162 |
|---|
| Numbering: | Vol. 727 |
|---|
| PID: | 20.500.12556/RUP-21611  |
|---|
| UDC: | 519.17 |
|---|
| ISSN on article: | 0024-3795 |
|---|
| DOI: | 10.1016/j.laa.2025.08.003 |
|---|
| COBISS.SI-ID: | 246729731 |
|---|
| Publication date in RUP: | 27.08.2025 |
|---|
| Views: | 433 |
|---|
| Downloads: | 5 |
|---|
| 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. |
