Khandhawit T.Pongtanapaisan P.Wasun A.Mahidol University2024-08-112024-08-112024-01-01Experimental Mathematics (2024)10586458https://repository.li.mahidol.ac.th/handle/20.500.14594/100428Two 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.MathematicsArticleSCOPUS10.1080/10586458.2024.23816812-s2.0-852005044341944950X