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Bounding the Openk-Monopoly Number of Strong Product Graphs

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Kuziak D., Peterin I., Yero I. G.

Discussiones Mathematicae Graph Theory

2017

tom 38

nr 1

287-299

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.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Kuziak D.

1 Peterin I.

1 Yero I. G.

1 2018

Wyniki wyszukiwania

Bounding the Openk-Monopoly Number of Strong Product Graphs