# Bled'11 - 7th Slovenian International Conference on Graph Theory

19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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# All generalized Petersen graphs are unit-distance graphs

Presented by Dr. Arjana ŽITNIK
Type: Oral presentation
Track: Representations of Graphs

## Content

In 1950 the class of generalized Petersen graphs was introduced by Coxeter and around 1970 popularized by Frucht, Graver and Watkins. The family of $I$-graphs mentioned in 1988 by Bouwer {\em et al.} represents a slight further albeit important generalization of the renowned Petersen graph. We show that each $I$-graph $I(n,j,k)$ admits a unit-distance representation in the Euclidean plane. This implies that each generalized Petersen graph admits a unit-distance representation in the Euclidean plane. In particular, we show that every $I$-graph $I(n,j,k)$ has an isomorphic $I$-graph that admits a unit-distance representation in the Euclidean plane with a $n$-fold rotational symmetry, with the exception of the families $I(n,j, j)$ and $I(12m,m, 5m)$, $m \ge 1$. We also provide unit-distance representations for these graphs.

## Place

Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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