Homomorphisms from the Coxeter graphOrel, Marko (Avtor) Višnjić, Draženka (Avtor) preserver problemssymmetric matricesinvertible matricesbinary fieldrankgraph homomorphismsCoxeter graphLet $S_n(\mathbb{F}_2)$ 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.20252025-08-27 09:12:02Članek v reviji21611UDK: 519.17ISSN pri članku: 0024-3795DOI: 10.1016/j.laa.2025.08.003COBISS.SI-ID: 246729731sl