- Tytuł:
- Upper Bounds on the Signed Total (k, k)-Domatic Number of Graphs
- Autorzy:
- Volkmann, Lutz
- Powiązania:
- https://bibliotekanauki.pl/articles/31339301.pdf
- Data publikacji:
- 2015-11-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
signed total (k
k)-domatic number
signed total k-dominating function
signed total k-domination number
regular graphs - Opis:
- Let $G$ be a graph with vertex set $V (G)$, and let $ f : V (G) \rightarrow {−1, 1}$ be a two-valued function. If $ k \geq 1$ is an integer and \( \sum_{ x \in N(v)} f(x) \geq k \) for each $ v \in V (G) $, where $N(v)$ is the neighborhood of $v$, then $f$ is a signed total $k$-dominating function on $G$. A set ${f_1, f_2, . . ., f_d}$ of distinct signed total k-dominating functions on $G$ with the property that \( \sum_{i=1}^d f_i(x) \leq k \) for each $ x \in V (G)$, is called a signed total ($k$, $k$)-dominating family (of functions) on $G$. The maximum number of functions in a signed total ($k$, $k$)-dominating family on $G$ is the signed total ($k$, $k$)-domatic number of $G$. In this article we mainly present upper bounds on the signed total ($k$, $k$)- domatic number, in particular for regular graphs.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2015, 35, 4; 641-650
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł