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Carlos A. Araujo
Universidad del Atlantico Km 7 Via Puerto Barranquilla Colombia
Electrical & Electronics Engineering

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Rainbow perfect domination in lattice graphs Luis R. Fuentes; Italo J. Dejter; Carlos A. Araujo
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 1 (2018): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2018.6.1.7

Abstract

Let 0 < n ∈ Z. In the unit distance graph of Zn ⊂ Rn, 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).
Co-Authors Italo J. Dejter Luis R. Fuentes