@article {
author = {Mostaghim, Zohreh and Ghaffari, Mohammad Hossein},
title = {Distance in cayley graphs on permutation groups generated by $k$ $m$-Cycles},
journal = {Transactions on Combinatorics},
volume = {6},
number = {3},
pages = {45-59},
year = {2017},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2017.21473},
abstract = {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 $\Omega^n_{k,m}$ be the set of all permutations of the form $c_1 c_2 \cdots c_k$ where $c_i$'s are arbitrary $m$-cycles in $S_n$. Suppose that $\Gamma^n_{k,m}$ be the Cayley graph on subgroup of $S_n$ generated by all permutations in $\Omega^n_{k,m}$. We find a shortest path joining identity and any vertex of $\Gamma^n_{k,m}$, 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. },
keywords = {permutation group,Cayley graph,Quadruple cycles,Diameter,Expressions of permutations},
url = {https://toc.ui.ac.ir/article_21473.html},
eprint = {https://toc.ui.ac.ir/article_21473_2e07c04c5fad360f2c8b9fc03265c648.pdf}
}