Planar Stick Indices of Some Knotted Graphs
Issued Date
2024-01-01
Resource Type
ISSN
10586458
eISSN
1944950X
Scopus ID
2-s2.0-85200504434
Journal Title
Experimental Mathematics
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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/20.500.14594/100428
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.