Involve: A Journal of Mathematics

  • Involve
  • Volume 9, Number 2 (2016), 333-345.

On closed graphs, II

David A. Cox and Andrew Erskine

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A graph is closed when its vertices have a labeling by [n] with a certain property first discovered in the study of binomial edge ideals. In this article, we explore various aspects of closed graphs, including the number of closed labelings and clustering coefficients.

Article information

Involve, Volume 9, Number 2 (2016), 333-345.

Received: 30 December 2014
Accepted: 5 April 2015
First available in Project Euclid: 22 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C75: Structural characterization of families of graphs
Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65] 05C78: Graph labelling (graceful graphs, bandwidth, etc.)

closed graph clustering coefficient


Cox, David A.; Erskine, Andrew. On closed graphs, II. Involve 9 (2016), no. 2, 333--345. doi:10.2140/involve.2016.9.333.

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  • D. A. Cox and A. Erskine, “On closed graphs, I”, Ars Combin. 120 (2015), 259–274.
  • M. Crupi and G. Rinaldo, “Binomial edge ideals with quadratic Gröbner bases”, Electron. J. Combin. 18:1 (2011), Paper 211.
  • V. Ene and A. Zarojanu, “On the regularity of binomial edge ideals”, Math. Nachr. 288:1 (2015), 19–24.
  • V. Ene, J. Herzog, and T. Hibi, “Cohen–Macaulay binomial edge ideals”, Nagoya Math. J. 204 (2011), 57–68.
  • V. Ene, J. Herzog, and T. Hibi, “Koszul binomial edge ideals”, pp. 125–136 in Bridging algebra, geometry, and topology, edited by D. Ibadula and W. Veys, Springer Proc. Math. Stat. 96, Springer, Cham, 2014.
  • V. Ene, J. Herzog, and T. Hibi, “Linear flags and Koszul filtrations”, Kyoto J. Math. 55:3 (2015), 517–530.
  • J. Herzog, T. Hibi, F. Hreinsdóttir, T. Kahle, and J. Rauh, “Binomial edge ideals and conditional independence statements”, Adv. in Appl. Math. 45:3 (2010), 317–333.
  • M. E. J. Newman, Networks: An introduction, Oxford University Press, 2010.
  • M. Ohtani, “Graphs and ideals generated by some 2-minors”, Comm. Algebra 39:3 (2011), 905–917.
  • S. Saeedi Madani and D. Kiani, “Binomial edge ideals of graphs”, Electron. J. Combin. 19:2 (2012), Paper 44.