On ve-quasi and secured ve-quasi independent sets of a graph
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DOI:
https://doi.org/10.26637/MJM0801/0019Abstract
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 setMathematics Subject Classification:
Mathematics- 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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