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ALL GENERALIZED PETERSEN GRAPHS ARE UNIT-DISTANCE GRAPHS
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 Title & Authors
ALL GENERALIZED PETERSEN GRAPHS ARE UNIT-DISTANCE GRAPHS
Zitnik, Arjana; Horvat, Boris; Pisanski, Tomaz;
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 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.
Dilation coefficient, plane-width, and resolution coefficient of graphs, Monatshefte für Mathematik, 2013, 170, 2, 179  crossref(new windwow)
2.
On the odd girth and the circular chromatic number of generalized Petersen graphs, Journal of Combinatorial Optimization, 2017, 33, 3, 897  crossref(new windwow)
3.
GI-graphs: a new class of graphs with many symmetries, Journal of Algebraic Combinatorics, 2014, 40, 1, 209  crossref(new windwow)
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