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Total restrained bondage in graphs |
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| Authors: | |
| Institution: | [1]Department of Mathematics, Shahrood University of Technology, 3619995161 Shahrood, Iran [2]Department of Mathematics, Faculty of Science and Technology, University Malaysia Terengganu, 21030 Kuala Terengganu, Terengganu, Malaysia [3]Department of Mathematics, Gdansk University of Technology, Narutowicza 11/12, 80-233, Gdadsk, Poland [4]Lehrstuhl II fuer Mathematik, RWTH Aachen University, 52056 Aachen, Germany |
| Abstract: | A subset S of vertices of a graph G with no isolated vertex is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex in V (G) S is also adjacent to a vertex in V (G) S. The total restrained domination number of G is the minimum cardinality of a total restrained dominating set of G. In this paper we initiate the study of total restrained bondage in graphs. The total restrained bondage number in a graph G with no isolated vertex, is the minimum cardinality of a subset of edges E such that G E has no isolated vertex and the total restrained domination number of G E is greater than the total restrained domination number of G. We obtain several properties, exact values and bounds for the total restrained bondage number of a graph. |
| Keywords: | Domination total restrained domination bondage |
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