On the $Q$-polynomial property of the full bipartite graph of a Hamming graph
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914761342451712 |
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| author | Fernández, Blas Maleki, Roghayeh Miklavič, Štefko Monzillo, Giusy |
| author_facet | Fernández, Blas Maleki, Roghayeh Miklavič, Štefko Monzillo, Giusy |
| contents | The $Q$-polynomial property is an algebraic property of distance-regular graphs, that was introduced by Delsarte in his study of coding theory. Many distance-regular graphs admit the $Q$-polynomial property. Only recently the $Q$-polynomial property has been generalized to graphs that are not necessarily distance-regular. In [ J. Combin. Theory Ser. A, 205:105872, 2024 ], it was shown that graphs arising from the Hasse diagrams of the so-called attenuated space posets are $Q$-polynomial. These posets could be viewed as $q$-analogs of the Hamming posets, which were not studied in [ J. Combin. Theory Ser. A, 205:105872, 2024 ]. The main goal of this paper is to fill this gap by showing that the graphs arising from the Hasse diagrams of the Hamming posets are $Q$-polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12510 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the $Q$-polynomial property of the full bipartite graph of a Hamming graph Fernández, Blas Maleki, Roghayeh Miklavič, Štefko Monzillo, Giusy Combinatorics 05E99, 05C50 The $Q$-polynomial property is an algebraic property of distance-regular graphs, that was introduced by Delsarte in his study of coding theory. Many distance-regular graphs admit the $Q$-polynomial property. Only recently the $Q$-polynomial property has been generalized to graphs that are not necessarily distance-regular. In [ J. Combin. Theory Ser. A, 205:105872, 2024 ], it was shown that graphs arising from the Hasse diagrams of the so-called attenuated space posets are $Q$-polynomial. These posets could be viewed as $q$-analogs of the Hamming posets, which were not studied in [ J. Combin. Theory Ser. A, 205:105872, 2024 ]. The main goal of this paper is to fill this gap by showing that the graphs arising from the Hasse diagrams of the Hamming posets are $Q$-polynomial. |
| title | On the $Q$-polynomial property of the full bipartite graph of a Hamming graph |
| topic | Combinatorics 05E99, 05C50 |
| url | https://arxiv.org/abs/2404.12510 |