| Title: | Homomorphisms from the Coxeter graph |
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| Authors: | ID Orel, Marko (Author)
ID Višnjić, Draženka (Author) |
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| Files: |  PDF - Presentation file, download (1,41 MB)
MD5: E25A887CEB0DE1A67FD03FC4DC031F26
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0024379525003398
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| 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. |
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| Keywords: | preserver problems, symmetric matrices, invertible matrices, binary field, rank, graph homomorphisms, Coxeter graph |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 15.12.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 129-162 |
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| Numbering: | Vol. 727 |
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| PID: | 20.500.12556/DiRROS-23969  |
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| UDC: | 519.17 |
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| ISSN on article: | 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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| Note: |
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| Publication date in DiRROS: | 28.10.2025 |
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| Views: | 214 |
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| Downloads: | 117 |
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| Metadata: |    |
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