JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ROMAN k-DOMINATION IN GRAPHS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
ROMAN k-DOMINATION IN GRAPHS
Kammerling, Karsten; Volkmann, Lutz;
  PDF(new window)
 Abstract
Let k be a positive integer, and let G be a simple graph with vertex set V (G). A Roman k-dominating function on G is a function f : V (G) {0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to at least k vertices with = 2 for i = 1, 2, , k. The weight of a Roman k-dominating function is the value f(V (G)) = f(u). The minimum weight of a Roman k-dominating function on a graph G is called the Roman k-domination number (G) of G. Note that the Roman 1-domination number (G) is the usual Roman domination number (G). In this paper, we investigate the properties of the Roman k-domination number. Some of our results extend these one given by Cockayne, Dreyer Jr., S. M. Hedetniemi, and S. T. Hedetniemi [2] in 2004 for the Roman domination number.
 Keywords
domination;Roman k-domination;Roman domination;kdomination;
 Language
English
 Cited by
1.
A CORRECTION TO A PAPER ON ROMAN κ-DOMINATION IN GRAPHS,;;

대한수학회보, 2013. vol.50. 2, pp.469-473 crossref(new window)
1.
A CORRECTION TO A PAPER ON ROMAN κ-DOMINATION IN GRAPHS, Bulletin of the Korean Mathematical Society, 2013, 50, 2, 469  crossref(new windwow)
2.
Data reductions and combinatorial bounds for improved approximation algorithms, Journal of Computer and System Sciences, 2016, 82, 3, 503  crossref(new windwow)
3.
k-Domination and k-Independence in Graphs: A Survey, Graphs and Combinatorics, 2012, 28, 1, 1  crossref(new windwow)
4.
The Roman k-domatic number of a graph, Acta Mathematica Sinica, English Series, 2011, 27, 10, 1899  crossref(new windwow)
5.
The Nk-valued Roman Domination and Its Boundaries, Electronic Notes in Discrete Mathematics, 2015, 48, 95  crossref(new windwow)
6.
A survey of Nordhaus–Gaddum type relations, Discrete Applied Mathematics, 2013, 161, 4-5, 466  crossref(new windwow)
7.
Relations between the Roman k-domination and Roman domination numbers in graphs, Discrete Mathematics, Algorithms and Applications, 2014, 06, 03, 1450045  crossref(new windwow)
 References
1.
E. W. Chambers, B. Kinnersley, N. Prince, and D. B. West, Extremal problems for Roman domination, unpublished manuscript, 2007.

2.
E. J. Cockayne, P. A. Dreyer Jr., S. M. Hedetniemi, and S. T. Hedetniemi, Roman domination in graphs, Discrete Math. 278 (2004), no. 1-3, 11-22. crossref(new window)

3.
E. J. Cockayne, P. J. P. Grobler, W. R. Grudnlingh, J. Munganga, and J. H. van Vuuren, Protection of a graph, Util. Math. 67 (2005), 19-32.

4.
J. F. Fink and M. S. Jacobson, n-domination in graphs, Graph theory with applications to algorithms and computer science (Kalamazoo, Mich., 1984), 283-300, Wiley-Intersci. Publ., Wiley, New York, 1985.

5.
J. F. Fink and M. S. Jacobson, On n-domination, n-dependence and forbidden subgraphs, Graph theory with applications to algorithms and computer science (Kalamazoo, Mich., 1984), 301-311, Wiley-Intersci. Publ., Wiley, New York, 1985.

6.
T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Fundamentals of Domination in Graphs, Monographs and Textbooks in Pure and Applied Mathematics, 208. Marcel Dekker, Inc., New York, 1998.

7.
T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Domination in Graphs: Advanced Topics, Monographs and Textbooks in Pure and Applied Mathematics, 209. Marcel Dekker, Inc., New York, 1998.

8.
C. S. ReVelle and K. E. Rosing, Defendens imperium romanum: a classical problem in military strategy, Amer. Math. Monthly 107 (2000), no. 7, 585-594. crossref(new window)

9.
I. Steward, Defend the Roman Empire!, Sci. Amer. 281 (1999), 136-139. crossref(new window)

10.
L. Volkmann, Graphen an allen Ecken und Kanten, RWTH Aachen 2006, XVI, 377 pp. http://www.math2.rwth-aachen.de/»uebung/GT/graphen1.html.