A dominating set S of a graph G is called efficient if |N[v]∩ S| = 1 for every vertex v ∈ V(G). That is, a dominating set S is efficient if and only if every vertex is dominated exactly once. In this paper, we investigate efficient multiple domination. There are several types of multiple domination defined in the literature: k-tuple domination, {k}-domination, and k-domination. We investigate efficient versions of the first two as well as a new type of multiple domination.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1371,
author = {Robert R. Rubalcaba and Peter J. Slater},
title = {Efficient (j,k)-domination},
journal = {Discussiones Mathematicae Graph Theory},
volume = {27},
year = {2007},
pages = {409-423},
zbl = {1142.05062},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1371}
}
Robert R. Rubalcaba; Peter J. Slater. Efficient (j,k)-domination. Discussiones Mathematicae Graph Theory, Tome 27 (2007) pp. 409-423. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1371/
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