| Naslov: | Homomorphisms from the Coxeter graph |
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| Avtorji: | ID Orel, Marko (Avtor)
ID Višnjić, Draženka (Avtor) |
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| Datoteke: |  RAZ_Orel_Marko_2025.pdf (1,42 MB)
MD5: B0CC923EA03D17B87A662B14EAB84B80
 https://www.sciencedirect.com/science/article/pii/S0024379525003398?via%3Dihub
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| Jezik: | Angleški jezik |
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| Vrsta gradiva: | Članek v reviji |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: | FAMNIT - Fakulteta za matematiko, naravoslovje in informacijske tehnologije
IAM - Inštitut Andrej Marušič
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| Opis: | 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. |
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| Ključne besede: | preserver problems, symmetric matrices, invertible matrices, binary field, rank, graph homomorphisms, Coxeter graph |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 07.08.2025 |
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| Leto izida: | 2025 |
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| Št. strani: | str. 129-162 |
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| Številčenje: | Vol. 727 |
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| PID: | 20.500.12556/RUP-21611  |
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| UDK: | 519.17 |
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| ISSN pri članku: | 0024-3795 |
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| DOI: | 10.1016/j.laa.2025.08.003 |
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| COBISS.SI-ID: | 246729731 |
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| Datum objave v RUP: | 27.08.2025 |
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| Število ogledov: | 434 |
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| Število prenosov: | 5 |
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| Metapodatki: |    |
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