A note on double domination in graphs
نویسندگان
چکیده
Recently, Haynes, Hedetniemi and Henning published the book Topics in Domination Graphs , which comprises 16 contributions that present advanced topics graph domination, featuring open problems, modern techniques, recent results. One of these is chapter Multiple by Hansberg Volkmann, where they put into context all relevant research results on multiple domination have been found up to 2020. In this note, we show how improve some double are included book.
منابع مشابه
Total double Roman domination in graphs
Let $G$ be a simple graph with vertex set $V$. A double Roman dominating function (DRDF) on $G$ is a function $f:Vrightarrow{0,1,2,3}$ satisfying that if $f(v)=0$, then the vertex $v$ must be adjacent to at least two vertices assigned $2$ or one vertex assigned $3$ under $f$, whereas if $f(v)=1$, then the vertex $v$ must be adjacent to at least one vertex assigned $2$ or $3$. The weight of a DR...
متن کاملA note on domination in bipartite graphs
DOMINATING SET remains NP -complete even when instances are restricted to bipartite graphs, however, in this case VERTEX COVER is solvable in polynomial time. Consequences to VECTOR DOMINATING SET as a generalization of both are discussed.
متن کاملOn Double Domination in Graphs
In a graph G, a vertex dominates itself and its neighbors. A subset S ⊆ V (G) is a double dominating set of G if S dominates every vertex of G at least twice. The minimum cardinality of a double dominating set of G is the double domination number γ×2(G). A function f(p) is defined, and it is shown that γ×2(G) = min f(p), where the minimum is taken over the n-dimensional cube C = {p = (p1, . . ....
متن کاملA Note on Total Domination Critical Graphs
The total domination number of G denoted by γt(G) is the minimum cardinality of a total dominating set of G. A graph G is total domination vertex critical or just γt-critical, if for any vertex v of G that is not adjacent to a vertex of degree one, γt(G − v) < γt(G). If G is γt-critical and γt(G) = k, then G is k-γt-critical. Haynes et al [The diameter of total domination vertex critical graphs...
متن کاملA note on domination and independence-domination numbers of graphs∗
Vizing’s conjecture is true for graphs G satisfying γ(G) = γ(G), where γ(G) is the domination number of a graph G and γ(G) is the independence-domination number of G, that is, the maximum, over all independent sets I in G, of the minimum number of vertices needed to dominate I . The equality γ(G) = γ(G) is known to hold for all chordal graphs and for chordless cycles of length 0 (mod 3). We pro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2021
ISSN: ['1872-6771', '0166-218X']
DOI: https://doi.org/10.1016/j.dam.2021.05.011