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Rainbow perfect domination in lattice graphs

L. Fuentes,I. Dejter,C. Araújo

Published 2018 in Electronic Journal of Graph Theory and Applications

ABSTRACT

Let $0<n\in\mathbb{Z}$. In the unit distance graph of $\mathbb{Z}^n\subset\mathbb{R}^n$, a perfect dominating set is understood as having induced components not necessarily trivial. A modification of that is proposed: a rainbow perfect dominating set , or RPDS, imitates a perfect-distance dominating set via a truncated metric; this has a distance involving at most once each coordinate direction taken as an edge color. Then, lattice-like RPDS s are built with their induced components C having: { i } vertex sets V(C) whose convex hulls are n-parallelotopes (resp., both (n-1)- and 0-cubes) and { ii } each V(C) contained in a corresponding   rainbow sphere  centered at C with radius n (resp., radii 1 and n-2).

PUBLICATION RECORD

  • Publication year

    2018

  • Venue

    Electronic Journal of Graph Theory and Applications

  • Publication date

    2018-04-03

  • Fields of study

    Mathematics, Physics, Computer Science

  • Identifiers
    DOI 10.5614/ejgta.2018.6.1.7
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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