Paths and circuits in g-graphs. (English) Zbl 1146.05306

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

Involve 1, No. 2, 135-144 (2008).

Summary: For a group \(G\) with generating set \(S = {s_1,s_2,\dots ,s_k}\), the \(G\)-graph of \(G\), denoted \(\Gamma (G,S)\), is the graph whose vertices are distinct cosets of \(\langle s_i\rangle\) 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 \(\Gamma (G,S)\).

MSC:

05C38	Paths and cycles
05C45	Eulerian and Hamiltonian graphs
05C25	Graphs and abstract algebra (groups, rings, fields, etc.)
20F05	Generators, relations, and presentations of groups

Keywords:

groups; graphs; generators; codets; Hamiltonian path; Eulerian path