Vol. 3, No. 2, 2010

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
$\mathbb{G}$-planar abelian groups

Andrea DeWitt, Jillian Hamilton, Alys Rodriguez and Jennifer Daniel

Vol. 3 (2010), No. 2, 233–240
Abstract

For a group G with generating set S = {s1,s2,,sk}, the G-graph of G, denoted by Γ(G,S), is the graph whose vertices are distinct cosets of si in G. Two distinct vertices are joined by an edge when the set intersection of the cosets is nonempty. In this paper, we explore the planarity of Γ(G,S).

Keywords
groups, graphs, generators
Mathematical Subject Classification 2000
Primary: 05C25, 20F05
Milestones
Received: 26 April 2010
Revised: 17 June 2010
Accepted: 24 June 2010
Published: 11 August 2010

Communicated by Scott Chapman
Authors
Andrea DeWitt
Lamar University
Department of Mathematics
Beaumont, TX 77710
United States
Jillian Hamilton
Lamar University
Department of Mathematics
Beaumont, TX 77710
United States
Alys Rodriguez
Lamar University
Department of Mathematics
Beaumont, TX 77710
United States
Jennifer Daniel
Lamar University
Department of Mathematics
Beaumont, TX 77710
United States