- Tytuł:
- On Minimal Geodetic Domination in Graphs
- Autorzy:
-
Nuenay, Hearty M.
Jamil, Ferdinand P. - Powiązania:
- https://bibliotekanauki.pl/articles/31339437.pdf
- Data publikacji:
- 2015-08-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
minimal geodetic dominating set
upper geodetic domination number - Opis:
- Let $G$ be a connected graph. For two vertices $u$ and $v$ in $G$, a $u$-$v$ geodesic is any shortest path joining $u$ and $v$. The closed geodetic interval $ I_G[u, v] $ consists of all vertices of $G$ lying on any $u$-$v$ geodesic. For $ S \subseteq V (G) $, $S$ is a geodetic set in $G$ if \( \bigcup_{u,v \in S} I_G [u, v] = V (G) \). Vertices $u$ and $v$ of $G$ are neighbors if $u$ and $v$ are adjacent. The closed neighborhood $ N_G[v]$ of vertex $v$ consists of $v$ and all neighbors of $v$. For $S \subseteq V (G)$, $S$ is a dominating set in $G$ if \( \bigcup_{u \in S} N_G[u] = V (G) \). A geodetic dominating set in $G$ is any geodetic set in $G$ which is at the same time a dominating set in $G$. A geodetic dominating set in $G$ is a minimal geodetic dominating set if it does not have a proper subset which is itself a geodetic dominating set in $G$. The maximum cardinality of a minimal geodetic dominating set in $G$ is the upper geodetic domination number of $G$. This paper initiates the study of minimal geodetic dominating sets and upper geodetic domination numbers of connected graphs.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2015, 35, 3; 403-418
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł