- Tytuł:
- Bounding the Open k-Monopoly Number of Strong Product Graphs
- Autorzy:
-
Kuziak, Dorota
Peterin, Iztok
Yero, Ismael G. - Powiązania:
- https://bibliotekanauki.pl/articles/31342423.pdf
- Data publikacji:
- 2018-02-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
open monopolies
strong product graphs
alliances
domination - Opis:
- Let $ G = (V, E) $ be a simple graph without isolated vertices and minimum degree $ \delta $, and let $ k \in \{ 1 − \ceil{ \delta // 2 }, . . ., \floor{ \delta // 2 } \} $ be an integer. Given a set $ M \subset V $, a vertex $ v $ of G is said to be $k$-controlled by $M$ if \( \delta_M (v) \ge \tfrac{ \delta G(v) }{2}+k \), where $ \delta_M(v) $ represents the number of neighbors of $v$ in $M$ and $ \delta_G(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.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2018, 38, 1; 287-299
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł