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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/2508.04137 |
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| _version_ | 1866909724136439808 |
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| author | Mondal, Priti Prasanna Kannan, M. Rajesh Atik, Fouzul |
| author_facet | Mondal, Priti Prasanna Kannan, M. Rajesh Atik, Fouzul |
| contents | This article investigates the isomorphism problem for graphs derived from the four standard graph products: Cartesian, Kronecker (direct), strong, and lexicographic product. We provide a complete characterization of all simple connected graphs for which their corresponding products are isomorphic. As a by-product, we identify a novel family of non-distance-regular graphs that possess fewer than d+1 distinct distance eigenvalues, where d represents the diameter of the graph. This result offers a new perspective on Problem 4.3 posed in [2], moving beyond the current approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04137 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | When Are Standard Graph Products Isomorphic? Mondal, Priti Prasanna Kannan, M. Rajesh Atik, Fouzul Combinatorics This article investigates the isomorphism problem for graphs derived from the four standard graph products: Cartesian, Kronecker (direct), strong, and lexicographic product. We provide a complete characterization of all simple connected graphs for which their corresponding products are isomorphic. As a by-product, we identify a novel family of non-distance-regular graphs that possess fewer than d+1 distinct distance eigenvalues, where d represents the diameter of the graph. This result offers a new perspective on Problem 4.3 posed in [2], moving beyond the current approaches. |
| title | When Are Standard Graph Products Isomorphic? |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2508.04137 |