#### Vol. 3, No. 2, 2010

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$\mathbb{G}$-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 $S=\left\{{s}_{1},{s}_{2},\dots ,{s}_{k}\right\}$, the $\mathbb{G}$-graph of $G$, denoted by $\Gamma \left(G,S\right)$, 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 explore the planarity of $\Gamma \left(G,S\right)$.

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