3,949 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
Upper bounds for domination related parameters in graphs on surfaces
AbstractIn this paper we give tight upper bounds on the total domination number, the weakly connected domination number and the connected domination number of a graph in terms of order and Euler characteristic. We also present upper bounds for the restrained bondage number, the total restrained bondage number and the restricted edge connectivity of graphs in terms of the orientable/nonorientable genus and maximum degree
Bounds on several versions of restrained domination number
We investigate several versions of restraineddomination numbers and present new bounds on these parameters. We generalize theconcept of restrained domination and improve some well-known bounds in the literature.In particular, for a graph of order and minimum degree , we prove thatthe restrained double domination number of is at most . In addition,for a connected cubic graph of order we show thatthe total restrained domination number of is at least andthe restrained double domination number of is at least
Restrained and Other Domination Parameters in Complementary Prisms.
In this thesis, we will study several domination parameters of a family of graphs known as complementary prisms. We will first present the basic terminology and definitions necessary to understand the topic. Then, we will examine the known results addressing the domination number and the total domination number of complementary prisms. After this, we will present our main results, namely, results on the restrained domination number of complementary prisms. Subsequently results on the distance - k domination number, 2-step domination number and stratification of complementary prisms will be presented. Then, we will characterize when a complementary prism is Eulerian or bipartite, and we will obtain bounds on the chromatic number of a complementary prism. We will finish the thesis with a section on possible future problems
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