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arXiv · 2603.25662

Isomorphic daisy cubes based on their $\tau$-graphs

Zhongyuan Che·Niko Tratnik·Petra Žigert Pleteršek
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Abstract

We prove that if $A$ and $B$ are daisy cubes whose $\tau$-graphs are forests, then $A$ and $B$ are isomorphic if and only if their $\tau$-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 $\tau$-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.

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Zhongyuan Che, Niko Tratnik, Petra Žigert Pleteršek. 2026-03-26. Isomorphic daisy cubes based on their $\tau$-graphs. https://arxiv.org/abs/2603.25662

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