%0 Report %A Derakhshan, Parisa %A Hussak, Walter %D 2015 %T Symmetry and optimality of disjoint Hamilton cycles in star graphs %U https://repository.lboro.ac.uk/articles/report/Symmetry_and_optimality_of_disjoint_Hamilton_cycles_in_star_graphs/9403481 %2 https://repository.lboro.ac.uk/ndownloader/files/17020118 %K Star graph %K Hamilton cycle %K Hamilton decomposition %K Automorphism %K Information and Computing Sciences not elsewhere classified %X Multiple edge-disjoint Hamilton cycles have been obtained in labelled star graphs Stn of degree n-1, using number-theoretic means, as images of a known base 2-labelled Hamilton cycle under label-mapping auto- morphisms of Stn. However, no optimum bounds for producing such edge-disjoint Hamilton cycles have been given, and no positive or nega- tive results exist on whether Hamilton decompositions can be produced by such constructions other than a positive result for St5. We show that for all even n there exist such collections, here called symmetric collec- tions, of φ(n)/2 edge-disjoint Hamilton cycles, where φ is Euler's totient function, and that this bound cannot be improved for any even or odd n. Thus, Stn is not symmetrically Hamilton decomposable if n is not prime. Our method improves on the known bounds for numbers of any kind of edge-disjoint Hamilton cycles in star graphs. %I Loughborough University