## Abstract

An orientation of an undirected graph G is an assignment of exactly one direction to each edge of G. Converting two-way traffic networks to one-way traffic networks and bidirectional communication networks to unidirectional communication networks are practical instances of graph orientations. In these contexts minimising the diameter of the resulting oriented graph is of prime interest. The n-star network topology was proposed as an alternative to the hypercube network topology for multiprocessor systems by Akers and Krishnamurthy [IEEE Trans. on Computers (1989)]. The n-star graph consists of n! vertices, each labelled with a distinct permutation of [n]. Two vertices are adjacent if their labels differ exactly in the first and one other position. is an vertex-transitive graph with diameter 3(n-1). Orientations of called unidirectional star graphs and distributed routing protocols over them were studied by Day and Tripathi [Information Processing Letters (1993)] and Fujita [The First International Symposium on Computing and Networking (CANDAR 2013)]. Fujita showed that the (directed) diameter of this unidirectional star graph is at most. In this paper, we propose a new distributed routing algorithm for the same analysed by Fujita, which routes a packet from any node s to any node t at an undirected distance d from s using at most hops. This shows that the (directed) diameter of is at most We also show that the diameter of is at least 2n when thereby showing that our upper bound is tight up to an additive factor.

Original language | English |
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Title of host publication | Algorithms and Discrete Applied Mathematics - 6th International Conference, CALDAM 2020, Proceedings |

Editors | Manoj Changat, Sandip Das |

Publisher | Springer |

Pages | 307-317 |

Number of pages | 11 |

ISBN (Print) | 9783030392185 |

DOIs | |

State | Published - 1 Jan 2020 |

Externally published | Yes |

Event | 6th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2020 - Hyderabad, India Duration: 13 Feb 2020 → 15 Feb 2020 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 12016 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 6th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2020 |
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Country/Territory | India |

City | Hyderabad |

Period | 13/02/20 → 15/02/20 |

## Keywords

- Oriented diameter
- Star graphs
- Strong orientation

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science