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Cayley digraphs and (1,j,n)-sequencings of the alternating groups An

✍ Scribed by Ronald J. Gould; Robert Roth

Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
703 KB
Volume
66
Category
Article
ISSN
0012-365X

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✦ Synopsis

The problem of finding a sequencing 1I 1, 112, • • •, HIAnl for the elements of the alternating group A,, which minimizes the cost function IAnl-1 c= Y~ c(nT~on~+l), i=1 where c(H)= [{j:/-/(J) #:J}l, is solved. For n/>3 the sequencing is constructed by finding a directed Hamiltonian path in the Cayley digraph Dn of A,, determined by the generating set Bn = {(1, j, n):j • {2, 3, ..., n -1}}. We further consider the question of finding a directed Hamiltonian cycle in D,,.

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