About m-domination number of graphs
Downloads
DOI:
https://doi.org/10.26637/MJM0702/0008Abstract
In this paper, we have defined the concept of m-dominating set in graphs. In order to define this concept we have used the notion of m-adjacent vertices. We have also defined the concepts of minimal m-dominating set, minimum m-dominating set and m-domination number which is the minimum cardinality of an m-dominating set. We prove that the complement of a minimal m-dominating set is an m-dominating set. Also we prove a necessary and sufficient condition under which the m-domination number increases or decreases when a vertex is removed from the graph. Further we have also studied the concept of m-removing a vertex from the graph and
we prove that the m-removal of a vertex from the graph always increases or does not change the m-domination number. Some examples have also been given.
Keywords:
m-dominating set, minimal m-dominating set, minimum m-dominating set, private m-neighbourhood of a vertex, m-removal of a vertexMathematics Subject Classification:
Mathematics- Pages: 177-181
- Date Published: 01-04-2019
- Vol. 7 No. 02 (2019): Malaya Journal of Matematik (MJM)
D. K. Thakkar and Neha P. Jamvecha, A New Variant of Edge Stability in Graphs, International Journal of Pure and Engg. Mathematics, 5(3)(2017), 87-97.
D. K. Thakkar and Neha P. Jamvecha, On mindependence in Graphs, International Journal of Scientific Reserach in Mathematical and Statistical Science, $5(4)(2018), 374-379$
E. Sampathkumar and P. S. Neeralagi, The neighbourhood number of a graph, Journal of Pure and Applied Mathematics, (1985), 126-136.
E. Sampathkumar and S. S. Kamath, Mixed Domination in Graphs, The Indian Journal of Statistics, (1992), 1223.
R. Laskar and K. Peters, Vertex and edge domination parameters in graphs, Congressus Numerantium, 48(1985), $291-305$
T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Domination in Graphs Advanced Topics, Marcel Dekker, Inc., New-York, 1998.
T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of domination in graphs, Marcel Dekker, Inc., New-York, 1998.
- NA
Similar Articles
- P. S. Reshmi, K. P. Jose , A queueing-inventory system with perishable items and retrial of customers , Malaya Journal of Matematik: Vol. 7 No. 02 (2019): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2019 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.