### Abstract

For a nontrivial knot K, Negami found an upper bound on the stick number s(K) in terms of its crossing number c(K) which is s(K) ≤ 2c(K). Later, Huh and Oh utilized the arc index α(K) to present a more precise upper bound s(K) ≤ 3/2c(K) + 3/2. Furthermore, Kim, No and Oh found an upper bound on the equilateral stick number s=(K) as follows; s=(K) ≤ 2c(K) + 2. As a sequel to this research program, we similarly define the stick number s(G) and the equilateral stick number s=(G) of a spatial graph G, and present their upper bounds as follows; [Equation presented here] [Equation presented here] where e and v are the number of edges and vertices of G, respectively, b is the number of bouquet cut-components, and k is the number of non-splittable components.

Original language | English |
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Article number | 1750100 |

Journal | Journal of Knot Theory and its Ramifications |

Volume | 26 |

Issue number | 14 |

DOIs | |

Publication status | Published - 2017 Dec 1 |

### Keywords

- Graph
- stick number
- upper bound

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

*Journal of Knot Theory and its Ramifications*,

*26*(14), [1750100]. https://doi.org/10.1142/S0218216517501000