Paths and circuits in 𝔾-graphs

Bauer, Christa; Johnson, Chrissy; Rodriguez, Alys; Temple, Bobby; Daniel, Jennifer

doi:10.2140/involve.2008.1.135

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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

DOI: 10.2140/involve.2008.1.135

Abstract

For a group $G$ with generating set $S = {s_{1}, s_{2}, \dots, s_{k}}$ , the $G$ -graph of $G$ , denoted $Γ (G, S)$ , is the graph whose vertices are distinct cosets of $〈 s_{i} 〉$ 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

Vol. 1, No. 2, 2008