| Title: | On commutative association schemes and associated (directed) graphs |
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| Authors: | ID Monzillo, Giusy (Author)
ID Penjić, Safet (Author) |
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| Files: |  RAZ_Monzillo_Giusy_2025.pdf (483,56 KB)
MD5: 2E879042E1B1DAEC669B54F3D013AA74
 https://www.combinatorics.org/ojs/index.php/eljc/article/view/v32i1p54
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FAMNIT - Faculty of Mathematics, Science and Information Technologies
IAM - Andrej Marušič Institute
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| Abstract: | Let ${\mathcal M}$ denote the Bose--Mesner algebra of a commutative $d$-class association scheme ${\mathfrak X}$ (not necessarily symmetric), and $\Gamma$ denote a (strongly) connected (directed) graph with adjacency matrix $A$. Under the assumption that $A$ belongs to ${\mathcal M}$, we describe the combinatorial structure of $\Gamma$. Moreover, we provide an algebraic-combinatorial characterization of $\Gamma$ when $A$ generates ${\mathcal M}$. Among else, we show that, if ${\mathfrak X}$ is a commutative $3$-class association scheme that is not an amorphic symmetric scheme, then we can always find a (directed) graph $\Gamma$ such that the adjacency matrix $A$ of $\Gamma$ generates the Bose--Mesner algebra ${\mathcal M}$ of ${\mathfrak X}$. |
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| Keywords: | commutative association schemes, association schemes, Bose-Mesner algebra, equitable partition, graphs generating schemes, quotient-polynomial graphs, x-distance-faithful intersection diagram |
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| Publication version: | Version of Record |
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| Publication date: | 28.03.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 1-38 |
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| Numbering: | Vol. 32, iss. 1, article no. P1.54 |
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| PID: | 20.500.12556/RUP-21794  |
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| UDC: | 519.17 |
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| ISSN on article: | 1077-8926 |
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| DOI: | 10.37236/12973 |
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| COBISS.SI-ID: | 231013635 |
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| Publication date in RUP: | 26.09.2025 |
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| Views: | 290 |
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| Downloads: | 4 |
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