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On Roman, Global and Restrained Domination in Graphs

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Abstract

In this paper, we present new upper bounds for the global domination and Roman domination numbers and also prove that these results are asymptotically best possible. Moreover, we give upper bounds for the restrained domination and total restrained domination numbers for large classes of graphs, and show that, for almost all graphs, the restrained domination number is equal to the domination number, and the total restrained domination number is equal to the total domination number. A number of open problems are posed.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of the West of England, Bristol, BS16 1QY, UK

    V. Zverovich & A. Poghosyan

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  1. V. Zverovich
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  2. A. Poghosyan
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Correspondence to V. Zverovich.

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Zverovich, V., Poghosyan, A. On Roman, Global and Restrained Domination in Graphs. Graphs and Combinatorics 27, 755–768 (2011). https://doi.org/10.1007/s00373-010-0992-z

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