The crossing number of chordal ring networks

Muhammad Imran, Muhammad Salman, Mezab-E-Rehmat, Imran Javaid

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


The chordal ring network of order n, denoted by CRn (x,y,z), is the graph with vertex set Zn, an additive group of integers modulo n, and adjacencies given by i ∼ i+x, i ∼ i+y, i ∼ i+z for all even vertex i and distinct odd integers x, y, z in [1, n-1]. The crossing number of a network(graph) is closely related to the minimum layout area required for the implementation of a VLSI circuit for that network. From this perspective, the analysis of crossing numbers of graphs makes most sense when one focuses on networks(graphs) that have good properties as interconnection networks. In this paper, we study the crossing number of the chordal ring networks CRn (1, 3, 9) for all even n ≥ 10.

Original languageEnglish
Pages (from-to)193-209
Number of pages17
JournalPeriodica Mathematica Hungarica
Issue number2
Publication statusPublished - Oct 15 2015
Externally publishedYes


  • Chordal ring
  • Crossing number
  • Good drawing
  • Optimal drawing
  • Planar graph

ASJC Scopus subject areas

  • General Mathematics


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