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Total restrained bondage in graphs

Acta Mathematica Sinica, English Series volume 29, pages 1033–1042 (2013)Cite this article

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.

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Authors and Affiliations

  1. Department of Mathematics, Shahrood University of Technology, 3619995161, Shahrood, Iran

    Nader Jafari Rad

  2. Department of Mathematics, Faculty of Science and Technology, University Malaysia Terengganu, 21030, Kuala Terengganu, Terengganu, Malaysia

    Roslan Hasni

  3. Department of Mathematics, Gdansk University of Technology, Narutowicza 11/12, 80-233, Gdańsk, Poland

    Joanna Raczek

  4. Lehrstuhl II für Mathematik, RWTH Aachen University, 52056, Aachen, Germany

    Lutz Volkmann

Authors
  1. Nader Jafari Rad
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  2. Roslan Hasni
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  3. Joanna Raczek
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  4. Lutz Volkmann
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Correspondence to Nader Jafari Rad.

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Jafari Rad, N., Hasni, R., Raczek, J. et al. Total restrained bondage in graphs. Acta. Math. Sin.-English Ser. 29, 1033–1042 (2013). https://doi.org/10.1007/s10114-013-1085-8

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  • DOI: https://doi.org/10.1007/s10114-013-1085-8

Keywords

  • Domination
  • total restrained domination
  • bondage

MR(2010) Subject Classification

  • 05C69