- Tytuł:
- The Double Roman Domatic Number of a Digraph
- Autorzy:
- Volkmann, Lutz
- Powiązania:
- https://bibliotekanauki.pl/articles/31348166.pdf
- Data publikacji:
- 2020-11-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
digraph
double Roman domination
double Roman domatic number - Opis:
- A double Roman dominating function on a digraph $D$ with vertex set $V(D)$ is defined in [G. Hao, X. Chen and L. Volkmann, Double Roman domination in digraphs, Bull. Malays. Math. Sci. Soc. (2017).] as a function $f : V (D) → {0, 1, 2, 3}$ having the property that if $f(v) = 0$, then the vertex $v$ must have at least two in-neighbors assigned 2 under $f$ or one in-neighbor w with $f(w) = 3$, and $if f(v) = 1$, then the vertex v must have at least one in-neighbor $u$ with $f(u) ≥ 2$. A set ${f_1, f_2, . . ., f_d}$ of distinct double Roman dominating functions on $D$ with the property that $∑_{i=1}^df_i(v)≤3$ for each $v ∈ V (D)$ is called a double Roman dominating family (of functions) on $D$. The maximum number of functions in a double Roman dominating family on $D$ is the double Roman domatic number of $D$, denoted by $d_{dR}(D)$. We initiate the study of the double Roman domatic number, and we present different sharp bounds on $d_{dR}(D)$. In addition, we determine the double Roman domatic number of some classes of digraphs.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2020, 40, 4; 995-1004
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł