Automorphisms generating disjoint Hamilton cycles in star graphs

by Derakhshan, Parisa

Type Thesis
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In the first part of the thesis we define an automorphism φn for each star graph Stn of degree n-1, which yields permutations of labels for the edges of Stn taken from the set of integers {1,..., [n/2c]}. By decomposing these permutations into permutation cycles, we are able to identify edge-disjoint Hamilton cycles that are automorphic images of a known two-labelled Hamilton cycle H1 2(n) in Stn. The search for edge-disjoint Hamilton cycles in star graphs is important for the design of interco…

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Summary

In the first part of the thesis we define an automorphism φn for each star graph Stn of degree n-1, which yields permutations of labels for the edges of Stn taken from the set of integers {1,..., [n/2c]}. By decomposing these permutations into permutation cycles, we are able to identify edge-disjoint Hamilton cycles that are automorphic images of a known two-labelled Hamilton cycle H1 2(n) in Stn. The search for edge-disjoint Hamilton cycles in star graphs is important for the design of interconnection network topologies in computer science. All our results improve on the known bounds for numbers of any kind of edge-disjoint Hamilton cycles in star graphs.

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Edition Statements

  • Publication Date:2015

Thesis Information

  • Degree:Ph.D.
  • University:Loughborough University

Publication Statements

  • Language:eng
  • Publication Date:2015

Edition Identifiers

  • ethos:647335

Subjects

Automorphism eng hamilton cycle Interconnection network topology PDF Star graph Symmetric group

Writers

Derakhshan, Parisa

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