About m-domination number of graphs

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DOI:

https://doi.org/10.26637/MJM0702/0008

Abstract

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 vertex

Mathematics Subject Classification:

Mathematics
  • D. K. Thakkar Department of Mathematics, Saurashtra University, Rajkot-360005, Gujarat, India.
  • P. Jamvecha Department of Mathematics, Saurashtra University, Rajkot-360005, Gujarat, India.
  • Pages: 177-181
  • Date Published: 01-04-2019
  • Vol. 7 No. 02 (2019): Malaya Journal of Matematik (MJM)

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Published

01-04-2019

How to Cite

D. K. Thakkar, and P. Jamvecha. “About M-Domination Number of Graphs”. Malaya Journal of Matematik, vol. 7, no. 02, Apr. 2019, pp. 177-81, doi:10.26637/MJM0702/0008.