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  • All generalized Petersen graphs are unit-distance graphs [Elektronski vir]
    Žitnik, Arjana ; Horvat, Boris, 1976- ; Pisanski, Tomaž
    In 1950 a 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 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.
    Vir: Preprint series [Elektronski vir]. - ISSN 2232-2094 (Vol. 48, št. 1109, 2010, str. 1-16)
    Vrsta gradiva - e-članek
    Leto - 2010
    Jezik - angleški
    COBISS.SI-ID - 15391321

    Povezava(-e):

    http://www.imfm.si/preprinti/PDF/01109.pdf

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