## Abstract

The chordal ring network of order n, denoted by CR_{n} (x,y,z), is the graph with vertex set Z_{n}, 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 CR_{n} (1, 3, 9) for all even n ≥ 10.

Original language | English |
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Pages (from-to) | 193-209 |

Number of pages | 17 |

Journal | Periodica Mathematica Hungarica |

Volume | 71 |

Issue number | 2 |

DOIs | |

Publication status | Published - Oct 15 2015 |

Externally published | Yes |

## Keywords

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

## ASJC Scopus subject areas

- Mathematics(all)