#### Vol. 1, No. 2, 2008

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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
##### Abstract

For a group $G$ with generating set $S=\left\{{s}_{1},{s}_{2},\dots ,{s}_{k}\right\}$, the $\mathbb{G}$-graph of $G$, denoted $\Gamma \left(G,S\right)$, 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 $\Gamma \left(G,S\right)$.

##### Keywords
Groups, graphs, generators
##### Mathematical Subject Classification 2000
Primary: 05C25, 20F05