20.500.12556/RUP-21611 Homomorphisms from the Coxeter graph 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. preserver problems symmetric matrices invertible matrices binary field rank graph homomorphisms Coxeter graph ohranjevalci simetrične matrike obrnljive matrike binarni obseg rang homomorfizmi grafov Coxeterjev graf true false true Angleški jezik Slovenski jezik Članek v reviji 2025-08-27 09:12:02 2025-08-27 09:12:04 2025-09-04 03:02:17 0000-00-00 00:00:00 2025 0 0 str. 129-162 Vol. 727 15 Dec. 2025 0000-00-00 Zaloznikova NiDoloceno apc 0000-00-00 0000-00-00 2025-08-07 519.17 0024-3795 10.1016/j.laa.2025.08.003 246729731 RAZ_Orel_Marko_2025.pdf RAZ_Orel_Marko_2025.pdf 1 B0CC923EA03D17B87A662B14EAB84B80 c8dd17ebb2f8cb0b1f9689d6629c47f809e6b5b1ea6fc959dcf19c1455c07b5b 61ee8d4f-8315-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31411 https://www.sciencedirect.com/science/article/pii/S0024379525003398?via%3Dihub 1 31a04ba6-8315-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31410 Fakulteta za matematiko, naravoslovje in informacijske tehnologije Inštitut Andrej Marušič 0 0 0