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arXiv · 2312.06603

Planar stick indices of some knotted graphs

Tirasan Khandhawit·Puttipong Pongtanapaisan·Athibadee Wasun
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Abstract

Two isomorphic graphs can have inequivalent spatial embeddings in 3-space. In this way, an isomorphism class of graphs contains many spatial graph types. A common way to measure the complexity of a spatial graph type is to count the minimum number of straight sticks needed for its construction in 3-space. In this paper, we give estimates of this quantity by enumerating stick diagrams in a plane. In particular, we compute the planar stick indices of knotted graphs with low crossing numbers. We also show that if a bouquet graph or a theta-curve has the property that its proper subgraphs are all trivial, then the planar stick index must be at least seven.

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Tirasan Khandhawit, Puttipong Pongtanapaisan, Athibadee Wasun. 2023-12-11. Planar stick indices of some knotted graphs. https://arxiv.org/abs/2312.06603

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