Let G = (V, E) be a simple graph without isolated vertices and minimum degree δ, and let k ∈ 1 − ⌈δ/2⌉, . . . , ⌊δ/2⌋ be an integer. Given a set M ⊂ V, a vertex v of G is said to be k-controlled by M if [...] δM(v)≥δG(v)2+k , where δM(v) represents the number of neighbors of v in M and δG(v) the degree of v in G. A set M is called an open k-monopoly if every vertex v of G is k-controlled by M. The minimum cardinality of any open k-monopoly is the open k-monopoly number of G. In this article we study the open k-monopoly number of strong product graphs. We present general lower and upper bounds for the open k-monopoly number of strong product graphs. Moreover, we study in addition the open 0-monopolies of several specific families of strong product graphs.
@article{bwmeta1.element.doi-10_7151_dmgt_2017,
author = {Dorota Kuziak and Iztok Peterin and Ismael G. Yero},
title = {Bounding the Openk-Monopoly Number of Strong Product Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {38},
year = {2018},
pages = {287-299},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_2017}
}
Dorota Kuziak; Iztok Peterin; Ismael G. Yero. Bounding the Openk-Monopoly Number of Strong Product Graphs. Discussiones Mathematicae Graph Theory, Tome 38 (2018) pp. 287-299. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_2017/