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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/2505.24358 |
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| _version_ | 1866916767767461888 |
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| author | Bitragunta, Abhinav Jadav, Hareshkumar Singh, Ranveer |
| author_facet | Bitragunta, Abhinav Jadav, Hareshkumar Singh, Ranveer |
| contents | We introduce a method for constructing larger families of connected cospectral graphs from two given cospectral families of sizes $p$ and $q$. The resulting family size depends on the Cartesian primality of the input graphs and can be one of $pq$, $p + q - 1$, or $\max(p, q)$, based on the strictness of the applied conditions. Under the strictest condition, our method generates $O(p^3q^3)$ new cospectral triplets, while the more relaxed conditions yield $\varOmega(pq^3 + qp^3)$ such triplets. We also use the existence of specific cospectral families to establish that of larger ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24358 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cartesian Prime Graphs and Cospectral Families Bitragunta, Abhinav Jadav, Hareshkumar Singh, Ranveer Discrete Mathematics We introduce a method for constructing larger families of connected cospectral graphs from two given cospectral families of sizes $p$ and $q$. The resulting family size depends on the Cartesian primality of the input graphs and can be one of $pq$, $p + q - 1$, or $\max(p, q)$, based on the strictness of the applied conditions. Under the strictest condition, our method generates $O(p^3q^3)$ new cospectral triplets, while the more relaxed conditions yield $\varOmega(pq^3 + qp^3)$ such triplets. We also use the existence of specific cospectral families to establish that of larger ones. |
| title | Cartesian Prime Graphs and Cospectral Families |
| topic | Discrete Mathematics |
| url | https://arxiv.org/abs/2505.24358 |