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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.03709 |
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| _version_ | 1866917896387559424 |
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| author | Shi, Minjia Wang, Lu Sole, Patrick |
| author_facet | Shi, Minjia Wang, Lu Sole, Patrick |
| contents | We show that the large Cartesian powers of any graph have log-concave valencies with respect to a ffxed vertex. We show that the series of valencies of distance regular graphs is log-concave, thus improving on a result of (Taylor, Levingston, 1978). Consequences for strongly regular graphs, two-weight codes, and completely regular codes are derived. By P-Q duality of association schemes the series of multiplicities of Q-polynomial association schemes is shown, under some assumption, to be log-concave. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03709 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The log concavity of two graphical sequences Shi, Minjia Wang, Lu Sole, Patrick Combinatorics Cryptography and Security We show that the large Cartesian powers of any graph have log-concave valencies with respect to a ffxed vertex. We show that the series of valencies of distance regular graphs is log-concave, thus improving on a result of (Taylor, Levingston, 1978). Consequences for strongly regular graphs, two-weight codes, and completely regular codes are derived. By P-Q duality of association schemes the series of multiplicities of Q-polynomial association schemes is shown, under some assumption, to be log-concave. |
| title | The log concavity of two graphical sequences |
| topic | Combinatorics Cryptography and Security |
| url | https://arxiv.org/abs/2501.03709 |