ALL GENERALIZED PETERSEN GRAPHS ARE UNIT-DISTANCE GRAPHS

- Journal title : Journal of the Korean Mathematical Society
- Volume 49, Issue 3, 2012, pp.475-491
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2012.49.3.475

Title & Authors

ALL GENERALIZED PETERSEN GRAPHS ARE UNIT-DISTANCE GRAPHS

Zitnik, Arjana; Horvat, Boris; Pisanski, Tomaz;

Zitnik, Arjana; Horvat, Boris; Pisanski, Tomaz;

Abstract

In 1950 a class of generalized Petersen graphs was introduced by Coxeter and around 1970 popularized by Frucht, Graver and Watkins. The family of -graphs mentioned in 1988 by Bouwer et al. represents a slight further albeit important generalization of the renowned Petersen graph. We show that each -graph 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 -graph has an isomorphic -graph that admits a unit-distance representation in the Euclidean plane with a -fold rotational symmetry, with the exception of the families and , . We also provide unit-distance representations for these graphs.

Keywords

unit-distance graph;I-graph;generalized Petersen graph;graph representation;degenerate representation;graph isomorphism;

Language

English

Cited by

1.

2.

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