Quasiperfect domination in triangular lattices

Details Quasiperfect domination in triangular lattices Quasiperfect domination in triangular lattices

2009-03-21

arxiv.org/abs/0903.3685v1

Discussiones Mathematicae Graph Theory 29(2009) 179-198

Mathematics

Combinatorics

20 pages, 9 figures, 5 arrays

Scientific paper

A vertex subset $S$ of a graph $G$ is a perfect (resp. quasiperfect) dominating set in $G$ if each vertex $v$ of $G\setminus S$ is adjacent to only one vertex ($d_v\in\{1,2\}$ vertices) of $S$. Perfect and quasiperfect dominating sets in the regular tessellation graph of Schl\"afli 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 $K_{\nu}$, where $\nu\in\{1,2,3\}$ depends only on $S$.

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