- Tytuł:
- General sharp upper bounds on the total coalition number
- Autorzy:
-
Barát, János
Blázsik, Zoltán - Tematy:
-
total domination
total coalition partition
total coalition number
total coalition graph - Pokaż więcej
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Powiązania:
- https://bibliotekanauki.pl/articles/59901678.pdf Link otwiera się w nowym oknie
- Opis:
- Let $G(V,E)$ be a finite, simple, isolate-free graph. Two disjoint sets $A,B\subset V$ form a total coalition in $G$, if none of them is a total dominating set, but their union $A\cup B$ is a total dominating set. A vertex partition $\Psi=\{C_1,C_2,...,C_k\}$ is a total coalition partition, if none of the partition classes is a total dominating set, meanwhile for every $i\in\{1,2,...,k\}$ there exists a distinct $j\in\{1,2,...,k\}$ such that $C_i$ and $C_j$ form a total coalition. The maximum cardinality of a total coalition partition of $G$ is the total coalition number of $G$ and denoted by $TC(G)$. We give a general sharp upper bound on the total coalition number as a function of the maximum degree. We further investigate this optimal case and study the total coalition graph. We show that every graph can be realised as a total coalition graph.
- Dostawca treści:
- Biblioteka Nauki
Artykuł