Arc index of spatial graphs

Min Jung Lee, Sungjong No, Seungsang Oh

Research output: Contribution to journalArticlepeer-review


Bae and Park found an upper bound on the arc index of prime links in terms of the minimal crossing number. In this paper, we extend the definition of the arc presentation to spatial graphs and find an upper bound on the arc index α(G) of any spatial graph G as α(G) ≤ c(G) + e + b where c (G) is the minimal crossing number of G, e is the number of edges, and b is the number of bouquet cut-components. This upper bound is lowest possible.

Original languageEnglish
Pages (from-to)406-415
Number of pages10
JournalJournal of Graph Theory
Issue number3
Publication statusPublished - 2019 Mar

Bibliographical note

Funding Information:
The second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Korean Ministry of Education (2009-0093827). The corresponding author (SO) was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea Government (MSIP) (no. NRF‐2017R1A2B2007216).

Funding Information:
National Research Foundation of Korea (NRF); Korean Ministry of Education, Grant/Award Number: 2009-0093827; Korea Government (MSIP), Grant/Award Number: NRF‐2017R1A2B2007216

Publisher Copyright:
© 2018 Wiley Periodicals, Inc.


  • arc index
  • spatial graph
  • upper bound

ASJC Scopus subject areas

  • Geometry and Topology


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