Planar Stick Indices of Some Knotted Graphs
2
Issued Date
2024-01-01
Resource Type
ISSN
10586458
eISSN
1944950X
Scopus ID
2-s2.0-85200504434
Journal Title
Experimental Mathematics
Rights Holder(s)
SCOPUS
Bibliographic Citation
Experimental Mathematics (2024)
Suggested Citation
Khandhawit T., Pongtanapaisan P., Wasun A. Planar Stick Indices of Some Knotted Graphs. Experimental Mathematics (2024). doi:10.1080/10586458.2024.2381681 Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/100428
Title
Planar Stick Indices of Some Knotted Graphs
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Author's Affiliation
Corresponding Author(s)
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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.