scholarly journals On the structure of Hamiltonian cycles in Cayley graphs of finite quotients of the modular group

1998 ◽  
Vol 204 (1-2) ◽  
pp. 233-248 ◽  
Author(s):  
Paul E. Schupp
Keyword(s):  
Modular Group ◽  
Cayley Graphs ◽  
Hamiltonian Cycles ◽  
Finite Quotients

scholarly journals Navigating directed Cayley graphs of small diameter: A potent Solovay–Kitaev procedure

2019 ◽  
Vol 29 (07) ◽  
pp. 1319-1342
Author(s):  
Henry Bradford
Keyword(s):  
Large Class ◽  
Finite Index ◽  
Fast Algorithm ◽  
Cayley Graphs ◽  
Small Diameter ◽  
Upper Bounds ◽  
Normal Subgroups ◽  
Generating Set ◽  
Finite Quotients

Let [Formula: see text] be a group and [Formula: see text] be a descending sequence of finite-index normal subgroups. We establish explicit upper bounds on the diameters of the directed Cayley graphs of the [Formula: see text], under some natural hypotheses on the behavior of power and commutator words in [Formula: see text]. The bounds we obtain do not depend on a choice of generating set. Moreover, under reasonable conditions our method provides a fast algorithm for navigating directed Cayley graphs. The proof is closely analogous to the Solovay–Kitaev procedure, which only uses commutator words, but also only constructs small-diameter undirected Cayley graphs. We apply our procedure to give new directed diameter bounds on finite quotients of a large class of regular branch groups, and of [Formula: see text] (for [Formula: see text] even).

scholarly journals Flows that are sums of hamiltonian cycles in Cayley graphs on abelian groups

2005 ◽  
Vol 299 (1-3) ◽  
pp. 208-268
Author(s):  
Dave Witte Morris ◽  
Joy Morris ◽  
David Petrie Moulton
Keyword(s):  
Abelian Groups ◽  
Cayley Graphs ◽  
Hamiltonian Cycles

Hamiltonian Cycles in Normal Cayley Graphs

2019 ◽  
Vol 35 (6) ◽  
pp. 1707-1714 ◽  
Author(s):  
Juan José Montellano-Ballesteros ◽  
Anahy Santiago Arguello
Keyword(s):  
Cayley Graphs ◽  
Hamiltonian Cycles ◽  
Normal Cayley Graphs

scholarly journals Hamiltonian cycles in Cayley graphs whose order has few prime factors

2011 ◽  
Vol 5 (1) ◽  
pp. 27-71 ◽  
Author(s):  
Klavdija Kutnar ◽  
Dragan Marušič ◽  
Dave Witte Morris ◽  
Joy Morris ◽  
Primož Šparl
Keyword(s):  
Cayley Graphs ◽  
Hamiltonian Cycles ◽  
Prime Factors

scholarly journals A survey: Hamiltonian cycles in Cayley graphs

1984 ◽  
Vol 51 (3) ◽  
pp. 293-304 ◽  
Author(s):  
David Witte ◽  
Joseph A. Gallian
Keyword(s):  
Cayley Graphs ◽  
Hamiltonian Cycles

Hamiltonian cycles in cubic Cayley graphs: the 〈2,4k,3〉 case

2009 ◽  
Vol 30 (4) ◽  
pp. 447-475 ◽  
Author(s):  
Henry H. Glover ◽  
Klavdija Kutnar ◽  
Dragan Marušič
Keyword(s):  
Cayley Graphs ◽  
Hamiltonian Cycles

scholarly journals On tetravalent normal edge-transitive Cayley graphs on the modular group

2017 ◽  
Vol 41 ◽  
pp. 1308-1312
Author(s):  
Hesam SHARIFI ◽  
Mohammad Reza DARAFSHEH
Keyword(s):  
Modular Group ◽  
Cayley Graphs ◽  
Edge Transitive

scholarly journals Hamiltonian cycles and paths in Cayley graphs and digraphs — A survey

1996 ◽  
Vol 156 (1-3) ◽  
pp. 1-18 ◽  
Author(s):  
Stephen J. Curran ◽  
Joseph A. Gallian
Keyword(s):  
Cayley Graphs ◽  
Hamiltonian Cycles
Sign in / Sign up

Export Citation Format

Share Document