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  Submitted to Discrete Mathematics Special Issue on

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by Marie-claude Heydemann, Nausica Marlin, Inria Projet Mascotte
http://www-sop.inria.fr/sloop/personnel/Nausica.Marlin/Publis/HMP00b.ps.gz
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Abstract:

As it is introduced by Bermond, Kodate, and P#rennes, some Cayley graphs, including most popular models for interconnection networks, admit a special automorphism, called complete rotation. Such an automorphism is often used to derive algorithms or properties of the underlying graph. For example, optimal gossiping algorithms can be easily designed, and the constructions of the best known edge disjoint spanning trees in the toroidal meshes and the hypercubes are based on such an automorphism. Our purpose is to characterize among Cayley graphs dened on a group generated by transpositions, which admit a complete rotation.

Citations

684 Graph Theory – Harary - 1971
194 A group-theoretic model for symmetric interconnection networks – Akers, Krishnamurthy - 1989
42 Symmetry in interconnection networks based on Cayley graphs of permutation groups: a survey – Lakshmivarahan, Jwo, et al. - 1993
38 Cayley graphs and interconnection networks – Heydemann - 1997
19 Arrangement graphs: a class of generalized star graphs – Day, Tripathi - 1992
12 Gossiping in Cayley graphs by packets – Bermond, Kodate, et al. - 1995
10 Line graphs and line digraphs – Hemminger, Beineke - 1978
6 Communication and fault tolerance algorithms on a class of interconnection networks – Fragopoulou - 1995
6 Cayley graphs with complete rotations – Heydemann, Marlin, et al. - 1997
5 Spanning graphs with applications to communication on a subclass of the Cayley graph based networks – Fragopoulou, Akl
4 Isomorphisms of transposition graphs – Delorme - 1997
2 Le groupe d'automorphismes des graphes de cayley engendr#s par des transpositions – Fournier - 1997
2 Diameter of some Cayley graphs – Sacl - 1997
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