Description of the First Disc Δ1 (t)of the Commuting Graph (G,X) for Elements of Order Three in Symmetric Groups.

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 Δ1 (t)-orbit representatives and the number of elements in the first disc Δ1 (t) of Δ1 (t), is studied when G is a symmetric group of degree n, Sym(n) and X is a conjugacy class of elements of order three. [ABSTRACT FROM AUTHOR]