On ve-quasi and secured ve-quasi independent sets of a graph

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DOI:

https://doi.org/10.26637/MJM0801/0019

Abstract

In this paper, we have defined the concepts of ve-quasi independent set and secured ve-quasi independent  set. In order to define these concepts we have used the concept of a vertex which m-dominates an edge. We  prove a characterization of a maximal ve-quasi independent set. We also prove that the complement of  a ve-quasi independent set is a ve-dominating set. We prove a necessary and sufficient condition under  which a ve-quasi independent set is a secured ve-quasi independent set. Also we prove a necessary and  sufficient condition under which the ve-quasi independence number and secured ve-quasi independence  number decrease when a vertex is removed from the graph. Some examples have also been given.

Keywords:

ve-quasi independent set, secured ve-quasi independent set, ve-quasi isolated vertex, ve-dominating set

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: 115-121
  • Date Published: 01-01-2020
  • Vol. 8 No. 01 (2020): Malaya Journal of Matematik (MJM)

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), $12-$ 19.

R. Laskar and K. Peters, Vertex and edge domination parameters in graphs, CongressusNumerantium, 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.

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Published

01-01-2020

How to Cite

D. K. Thakkar, and P. Jamvecha. “On Ve-Quasi and Secured Ve-Quasi Independent Sets of a Graph”. Malaya Journal of Matematik, vol. 8, no. 01, Jan. 2020, pp. 115-21, doi:10.26637/MJM0801/0019.