International Journal of Mathematics Trends and Technology
Volume 37 | Number 4 | Year 2016 | Article Id. IJMTT-V37P536 | DOI : https://doi.org/10.14445/22315373/IJMTT-V37P536
The concept of a Restrained set was defined in [1]. A set S of a vertices of a graph G is called a ‘Restrained set’if for every vertex v not is S there is a vertex u not in S such that u is adjacent to v. In this paper we consider the effect of removing an edge from the graph on the restrainedness number. We prove necessary and sufficient conditions under which this number increases or decreases when an edge is removed from the graph. Also we show that when this number decreases, it decreases by 2 and when it increases, it increases by 2.
[1] D.K.Thakkar and B.M.Kakrech, Maximal Restrained Sets In Graphs, International Journal of Mathematics and Soft Computing, Volume 4 Issue 2, 2014, 207-211.
[2] G.S.Domke, J.H.Hettingh, S.T.Hedetniemi, R.C.Laskar and L.R.Markus, Restrained domination in graphs, Discrete Math. 203(1999), 61-69.
[3] T.W.Haynes, S.T.Hedetniemi and P.J.Slater, FUNDAMENTAL OF DOMINATION IN GRAPHS, Marcel Dekker, Inc., New York, (1998).
[4] T.W.Haynes, S.T.Hedetniemi and P.J.Slater, DOMINATION IN GRAPHS ADVANCED TOPICS, Marcel Dekker, Inc., New York, (1998).
D.K.Thakkar, S.M.Badiyani, "Edge Deletion and Restrained Sets in Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 37, no. 4, pp. 260-262, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V37P536
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