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arXiv · 2505.24358

Cartesian Prime Graphs and Cospectral Families

Abhinav Bitragunta·Hareshkumar Jadav·Ranveer Singh
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Abstract

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.

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Abhinav Bitragunta, Hareshkumar Jadav, Ranveer Singh. 2025-05-30. Cartesian Prime Graphs and Cospectral Families. https://arxiv.org/abs/2505.24358

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