Isomorphic daisy cubes based on their $τ$-graphs
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910076024913920 |
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| author | Che, Zhongyuan Tratnik, Niko Pleteršek, Petra Žigert |
| author_facet | Che, Zhongyuan Tratnik, Niko Pleteršek, Petra Žigert |
| contents | We prove that if $A$ and $B$ are daisy cubes whose $τ$-graphs are forests, then $A$ and $B$ are isomorphic if and only if their $τ$-graphs are isomorphic. The result is applied to show that a daisy cube with at least one edge is the resonance graph of a plane bipartite graph $G$ if and only if its $τ$-graph is a forest which is isomorphic to the inner dual of the subgraph of $G$ obtained by removing all forbidden edges. As a consequence, some well known properties of Fibonacci cubes and Lucas cubes are provided as examples with different proofs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_25662 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Isomorphic daisy cubes based on their $τ$-graphs Che, Zhongyuan Tratnik, Niko Pleteršek, Petra Žigert Combinatorics 05C60 05C75 05C12 05C10 05C70 05C76 05C92 05C05 We prove that if $A$ and $B$ are daisy cubes whose $τ$-graphs are forests, then $A$ and $B$ are isomorphic if and only if their $τ$-graphs are isomorphic. The result is applied to show that a daisy cube with at least one edge is the resonance graph of a plane bipartite graph $G$ if and only if its $τ$-graph is a forest which is isomorphic to the inner dual of the subgraph of $G$ obtained by removing all forbidden edges. As a consequence, some well known properties of Fibonacci cubes and Lucas cubes are provided as examples with different proofs. |
| title | Isomorphic daisy cubes based on their $τ$-graphs |
| topic | Combinatorics 05C60 05C75 05C12 05C10 05C70 05C76 05C92 05C05 |
| url | https://arxiv.org/abs/2603.25662 |