|
|
|
|
distance in cayley graphs on permutation groups generated by k m-cycles
|
|
|
|
|
|
|
|
نویسنده
|
mostaghim zohreh ,ghaffari mohammad hossein
|
|
منبع
|
transactions on combinatorics - 2017 - دوره : 6 - شماره : 3 - صفحه:45 -59
|
|
چکیده
|
in this paper, we extend upon the results of b. suceav{u{a}} and r. stong [amer. math. monthly, 110 (2003) 162--162], which they computed the minimum number of 3-cycles needed to generate an even permutation.let ωnk,m be the set of all permutations of the form c1c2⋯ck where ci's are arbitrary m-cycles in sn. suppose that γnk,m be the cayley graph on subgroup of sn generated by all permutations in ωnk,m. we find a shortest path joining identity and any vertex of γnk,m, for arbitrary natural number k, and m=2,,3,,4. also, we calculate the diameter of these cayley graphs. as an application, we present an algorithm for finding a short expression of a permutation as products of given permutations.
|
|
کلیدواژه
|
permutation group ,cayley graph ,quadruple cycles ,diameter ,expressions of permutations.
|
|
آدرس
|
iran university of science and technology, school of mathematics, cryptography and data security laboratory,, ایران, iran university of science and technology, school of mathematics, ایران
|
|
پست الکترونیکی
|
mhghaffari@iust.ac.ir
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Authors
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|