Bounding the Openk-Monopoly Number of Strong Product Graphs

• Autorzy: Dorota Kuziak , Iztok Peterin , Ismael G. Yero
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

open monopolies; strong product graphs; alliances; domination

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques
• 05C76: Graph operations (line graphs, products, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2017
• Tom: 38
• Numer: 1
• Strony: 287-299

Daty

wydano

2018-02-01

otrzymano

2015-11-26

poprawiono

2016-12-15

zaakceptowano

2016-12-19

online

2017-12-30

Twórcy

autor

Dorota Kuziak

• , , Av. Ramón Puyol s/n, ,

autor

Iztok Peterin

• , , Koroška 46, , ; , Jadranska 19, ,

autor

Ismael G. Yero

• , , Av. Ramón Puyol s/n, ,

Identyfikatory

DOI

10.7151/dmgt.2017