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arXiv · 2404.07819

Generation of $3$-connected, planar line graphs

Phoebe Hollowbread-Smith·Riccardo W. Maffucci
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Abstract

We classify and construct all line graphs that are $3$-polytopes (planar and $3$-connected). Apart from a few special cases, they are all obtained starting from the medial graphs of cubic (i.e., $3$-regular) $3$-polytopes, by applying two types of graph transformations. This is similar to the generation of other subclasses of $3$-polytopes.

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Phoebe Hollowbread-Smith, Riccardo W. Maffucci. 2024-04-11. Generation of $3$-connected, planar line graphs. https://arxiv.org/abs/2404.07819

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