Vol. 1, No. 2, 2008

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Paths and circuits in $\mathbb{G}$-graphs

Christa Marie Bauer, Chrissy Konecia Johnson, Alys Monell Rodriguez, Bobby Dean Temple and Jennifer Renee Daniel

Vol. 1 (2008), No. 2, 135–144
Abstract

For a group G with generating set S = {s1,s2,,sk}, the G-graph of G, denoted 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 study the existence of Hamiltonian and Eulerian paths and circuits in Γ(G,S).

Keywords
Groups, graphs, generators
Mathematical Subject Classification 2000
Primary: 05C25, 20F05
Milestones
Received: 4 February 2008
Revised: 9 April 2008
Accepted: 2 June 2008
Published: 1 July 2008

Communicated by Scott Chapman
Authors
Christa Marie Bauer
Department of Mathematics
Lamar University
Beaumont, TX 77710
United States
Chrissy Konecia Johnson
Electronic Engineering Technology Department
Fort Valley State University
Fort Valley, GA 31030
United States
Alys Monell Rodriguez
Department of Mathematics
Lamar University
Beaumont, TX 77710
United States
Bobby Dean Temple
Department of Mathematics
Lamar University
Beaumont, TX 77710
United States
Jennifer Renee Daniel
Department of Mathematics
Lamar University
Beaumont, TX 77710
United States