42 research outputs found
On Roman, Global and Restrained Domination in Graphs
In this paper, we present new upper bounds for the global domination and Roman domination numbers and also prove that these results are asymptotically best possible. Moreover, we give upper bounds for the restrained domination and total restrained domination numbers for large classes of graphs, and show that, for almost all graphs, the restrained domination number is equal to the domination number, and the total restrained domination number is equal to the total domination number. A number of open problems are posed. © 2010 Springer
Integer Programming Formulations and Probabilistic Bounds for Some Domination Parameters
In this paper, we further study the concepts of hop domination and 2-step
domination and introduce the concepts of restrained hop domination, total
restrained hop domination, 2-step restrained domination, and total 2-step
restrained domination in graphs. We then construct integer programming
formulations and present probabilistic upper bounds for these domination
parameters
Remarks on restrained domination and total restrained domination in graphs
summary:The restrained domination number and the total restrained domination number of a graph were introduced recently by various authors as certain variants of the domination number of . A well-known numerical invariant of a graph is the domatic number which is in a certain way related (and may be called dual) to . The paper tries to define analogous concepts also for the restrained domination and the total restrained domination and discusses the sense of such new definitions
Remarks on restrained domination and total restrained domination in graphs
The restrained domination number γ r(G) and the total restrained domination number γ t r (G) of a graph G were introduced recently by various authors as certain variants of the domination number γ(G) of (G). A well-known numerical invariant of a graph is the domatic number d(G) which is in a certain way related (and may be called dual) to γ(G). The paper tries to define analogous concepts also for the restrained domination and the total restrained domination and discusses the sense of such new definitions. © Mathematical Institute, Academy of Sciences of Czech Republic 2005
DETERMINATION OF THE RESTRAINED DOMINATION NUMBER ON VERTEX AMALGAMATION AND EDGE AMALGAMATION OF THE PATH GRAPH WITH THE SAME ORDER
Graph theory is a mathematics section that studies discrete objects. One of the concepts studied in graph theory is the restrained dominating set which aims to find the restrained dominating number. This research was conducted by examining the graph operation result of the vertex and edges amalgamation of the path graph in the same order. The method used in this research is the deductive method by using existing theorems to produce new theorems that will be proven deductively true. This research aimed to determine the restrained dominating number in vertex and edges amalgamation of the path graph in the same order. The results obtained from this study are in the form of the theorem about the restrained dominating number of vertex and edges amalgamation of the path graph in the same order, namely: for , ⌋, and for , ⌋
Fair Restrained Dominating Set in the Corona of Graphs
In this paper, we give the characterization of a fair restrained dominating set in the corona of two nontrivial connected graphs and give some important results