Perfect Domination in Knights Graphs

Todd Fenstermacher; Soumendra Ganguly; Renu Laskar

Perfect Domination in Knights Graphs

Combinatorics 2018-05-10 v1

Authors: Todd Fenstermacher , Soumendra Ganguly , Renu Laskar

Abstract

For a graph $G = (V,E),$ a subset $S$ of $V$ is a perfect dominating set of $G$ if every vertex not in $S$ is adjacent to exactly one vertex in $S.$ The perfect domination number, $\gamma_p(G),$ is the minimum cardinality of a perfect dominating set of $G.$ The perfect domination number is found for knights graphs on square, rectangular, and infinite chessboards. Indeed, exact values or bounds are given for all chessboards except those with 3 rows and number of columns congruent to 1, 2, or 3 modulo 8.

Keywords

domination in graphs

Cite

@article{arxiv.1805.03335,
  title  = {Perfect Domination in Knights Graphs},
  author = {Todd Fenstermacher and Soumendra Ganguly and Renu Laskar},
  journal= {arXiv preprint arXiv:1805.03335},
  year   = {2018}
}

Comments

A portion of these results were presented at the 49th SE International Conference on Combinatorics, Graph Theory and Computing, March 5-9, 2018 and will appear in the conference proceedings, Congressus Numerantium (2018)

Perfect Domination in Knights Graphs

Abstract

Keywords

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