On coherent configuration of circular-arc graphs
For any graph, Weisfeiler and Leman assigned the smallest matrix algebra which contains the adjacency matrix of the graph. The coherent configuration underlying this algebra for a graph $\Gamma$ is called the coherent configuration of $\Gamma$, denoted by $\mathcal{X}(\Gamma)$. In this paper,...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Azarbaijan Shahide Madani University
2025-03-01
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| Series: | Communications in Combinatorics and Optimization |
| Subjects: | |
| Online Access: | https://comb-opt.azaruniv.ac.ir/article_14629_d9f1f125040619de623f0d486b420b49.pdf |
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| Summary: | For any graph, Weisfeiler and Leman assigned the smallest matrix algebra which
contains the adjacency matrix of the graph. The coherent configuration underlying this algebra for a graph $\Gamma$ is called the coherent configuration of $\Gamma$, denoted by $\mathcal{X}(\Gamma)$.
In this paper, we study the coherent configuration of circular-arc graphs. We give a characterization of the
circular-arc graphs $\Gamma$, where $\mathcal{X}(\Gamma)$ is a homogeneous coherent configuration. Moreover, all
homogeneous coherent configurations which are obtained in this way
are characterized as a subclass of Schurian coherent configurations. |
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| ISSN: | 2538-2128 2538-2136 |