# Bounding the Openk-Monopoly Number of Strong Product Graphs

Dorota Kuziak; Iztok Peterin; Ismael G. Yero

Discussiones Mathematicae Graph Theory (2018)

- Volume: 38, Issue: 1, page 287-299
- ISSN: 2083-5892

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topDorota Kuziak, Iztok Peterin, and Ismael G. Yero. "Bounding the Openk-Monopoly Number of Strong Product Graphs." Discussiones Mathematicae Graph Theory 38.1 (2018): 287-299. <http://eudml.org/doc/288387>.

@article{DorotaKuziak2018,

abstract = {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 $\delta _M (v) \ge \{\{\delta _G (v)\} \over 2\} + k$ , 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.},

author = {Dorota Kuziak, Iztok Peterin, Ismael G. Yero},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {open monopolies; strong product graphs; alliances; domination},

language = {eng},

number = {1},

pages = {287-299},

title = {Bounding the Openk-Monopoly Number of Strong Product Graphs},

url = {http://eudml.org/doc/288387},

volume = {38},

year = {2018},

}

TY - JOUR

AU - Dorota Kuziak

AU - Iztok Peterin

AU - Ismael G. Yero

TI - Bounding the Openk-Monopoly Number of Strong Product Graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2018

VL - 38

IS - 1

SP - 287

EP - 299

AB - 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 $\delta _M (v) \ge {{\delta _G (v)} \over 2} + k$ , 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.

LA - eng

KW - open monopolies; strong product graphs; alliances; domination

UR - http://eudml.org/doc/288387

ER -

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