The commuting graph C(G, X), where G is a finite group and X is a subset of G, is the graph whose vertex set is X and two distinct elements of X being joined by an edge whenever they commute in the group G. Here the CG(t)-orbit representatives and the number of elements in the first disc Δ1(t) of C(G, X), is studied when G is a symmetric group of degree n, Sym(n) and X is a conjugacy class of elements of order three.
REFERENCES
1.
A.
Nawawi
, “Commuting Graphs for Elements of Order Three in Finite Groups
,” Ph.D. thesis, The University of Manchester
, United Kingdom
, 2013
.2.
A.
Nawawi
and P.
Rowley
, The Electronic Journal of Combinatorics
22
(1
), #P1.21
(2015
).3.
C.
Bates
, D.
Bundy
, S.
Perkins
and P.
Rowley
, J. Algebra
266
(1
), 133
–153
(2003
).4.
C.
Bates
, D.
Bundy
, S.
Perkins
and P.
Rowley
, J. Group Theory
6
(4
), 461
–476
(2003
).5.
C.
Bates
, D.
Bundy
, S.
Perkins
and P.
Rowley
, Comm. Algebra
32
(11
), 4179
–4196
(2004
).6.
C.
Bates
, D.
Bundy
, S.
Hart
and P.
Rowley
, J. Algebra
316
(2
), 849
–868
(2007
).7.
W.
Bosma
, J. J.
Cannon
and C.
Playoust
, J. Symbolic Comput.
24
(3–4
), 235
–265
(1997
).
This content is only available via PDF.
© 2016 Author(s).
2016
Author(s)
You do not currently have access to this content.
