Results 51 to 60 of about 6,662,662 (243)

Equality of total domination and chromatic total domination in graphs

International journal of health sciences, 2022
Let  be a simple, finite and undirected graph and without isolated vertex. A subset D of V is said to be dominating set if for every  in  there exist a vertex  in  such that  and  are adjacent. The minimum cardinality of a dominating set of  is called the domination number of  and is denoted by .
M. Angala Eswari, S. Balamurugan
openaire   +1 more source

Domination Analysis of Greedy Heuristics For The Frequency Assignment Problem [PDF]

, 2003
We introduce the greedy expectation algorithm for the fixed spectrum version of the frequency assignment problem. This algorithm was previously studied for the travelling salesman problem.
Noble, SD, Noble, Steven, A.E. Koller, Koller, A.E., Noble, S.D., S.D. Noble, Koller, AE   +6 more
core   +1 more source

Total domination and least domination in a tree

Discrete Mathematics, 2003
A subset \(X\) of the vertex set \(V(G)\) of a graph \(G\) is called dominating (or total dominating) in \(G\), if for each \(x\in V(G)- X\) (or for each \(x\in V(G)\), respectively) there exists \(y\in X\) adjacent to \(x\). The least number of vertices of a dominating (or total dominating) set in \(G\) is the domination number \(\gamma(G)\) (or the ...
Xuezheng Lv, Jingzhong Mao
openaire   +1 more source

Total Dominator Colorings in Paths [PDF]

, 2012
Determining the total dominator chromatic number in ...
Vijayalekshmi, A., A. Vijayalekshmi
core   +1 more source

On the Complexity of Reinforcement in Graphs

Discussiones Mathematicae Graph Theory, 2016
We show that the decision problem for p-reinforcement, p-total rein- forcement, total restrained reinforcement, and k-rainbow reinforcement are NP-hard for bipartite graphs.
Rad Nader Jafari
doaj   +1 more source

On a conjecture concerning total domination subdivision number in graphs

AKCE International Journal of Graphs and Combinatorics, 2021
Let be the total domination number and let be the total domination subdivision number of a graph G with no isolated vertex. In this paper, we show that for some classes of graphs G, which partially solve the conjecture presented by Favaron et al.
S. Kosari, Z. Shao, R. Khoeilar, H. Karami, S. M. Sheikholeslami, G. Hao   +5 more
doaj   +1 more source

Total 2-Rainbow Domination in Graphs

Mathematics, 2022
A total k-rainbow dominating function on a graph G=(V,E) is a function f:V(G)→2{1,2,…,k} such that (i) ∪u∈N(v)f(u)={1,2,…,k} for every vertex v with f(v)=∅, (ii) ∪u∈N(v)f(u)≠∅ for f(v)≠∅.
Huiqin Jiang, Yongsheng Rao
doaj   +1 more source

Some notes on the isolate domination in graphs

AKCE International Journal of Graphs and Combinatorics, 2017
A subset of vertices of a graph is a dominating set of if every vertex in has a neighbor in . The domination number is the minimum cardinality of a dominating set of . A dominating set is an isolate dominating set if the induced subgraph has at least one
Nader Jafari Rad
doaj   +1 more source

Total Roman Domination Number of Rooted Product Graphs

Mathematics, 2020
Let G be a graph with no isolated vertex and f:V(G)→{0,1,2} a function. If f satisfies that every vertex in the set {v∈V(G):f(v)=0} is adjacent to at least one vertex in the set {v∈V(G):f(v)=2}, and if the subgraph induced by the set {v∈V(G):f(v)≥1} has ...
Abel Cabrera Martínez, Suitberto Cabrera García, Andrés Carrión García, Frank A. Hernández Mira   +3 more
doaj   +1 more source

Lower Bounds for the Total Distance $k$-Domination Number of a Graph

Theory and Applications of Graphs
For $k \geq 1$ and a graph $G$ without isolated vertices, a \emph{total distance $k$-dominating set} of $G$ is a set of vertices $S \subseteq V(G)$ such that every vertex in $G$ is within distance $k$ to some vertex of $S$ other than itself.
Randy R. Davila
doaj   +1 more source