Discussiones Mathematicae Graph Theory 29(1) (2009) 179-198
doi: 10.7151/dmgt.1439

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Italo J. Dejter

University of Puerto Rico
Rio Piedras, PR 00931-3355
e-mail: ijdejter@uprrp.edu


A vertex subset S of a graph G is a perfect (resp. quasiperfect) dominating set in G if each vertex v of G∖S is adjacent to only one vertex (dv ∈ {1,2} vertices) of S. Perfect and quasiperfect dominating sets in the regular tessellation graph of Schläfli symbol {3,6} and in its toroidal quotients are investigated, yielding the classification of their perfect dominating sets and most of their quasiperfect dominating sets S with induced components of the form Kν, where ν ∈ {1,2,3} depends only on S.

Keywords: perfect dominating set, quasiperfect dominating set, triangular lattice.

2000 Mathematics Subject Classification: Primary: 05C69;
Secondary: 68R10.


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Received 28 April 2008
Revised 8 December 2008
Accepted 16 December 2008