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Bounds on the Connected Forcing Number of a Graph

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Abstract

In this paper, we study (zero) forcing sets which induce connected subgraphs of a graph. The minimum cardinality of such a set is called the connected forcing number of the graph. We provide sharp upper and lower bounds on the connected forcing number in terms of the minimum degree, maximum degree, girth, and order of the graph.

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Notes

  1. This invariant is concurrently introduced in [5].

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Acknowledgements

The authors express their sincere thanks to an anonymous referee for his/her meticulous and thorough reading of the paper that greatly improved the exposition and clarity of the manuscript.

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Authors and Affiliations

  1. Department of Pure and Applied Mathematics, University of Johannesburg, Auckland Park, 2006, South Africa

    Randy Davila & Michael A. Henning

  2. Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, 30458, USA

    Colton Magnant

  3. Department of Mathematics and Statistics, University of Houston–Downtown, Houston, TX, 77002, USA

    Randy Davila & Ryan Pepper

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  1. Randy Davila
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  2. Michael A. Henning
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  3. Colton Magnant
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  4. Ryan Pepper
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Correspondence to Randy Davila.

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Davila, R., Henning, M.A., Magnant, C. et al. Bounds on the Connected Forcing Number of a Graph. Graphs and Combinatorics 34, 1159–1174 (2018). https://doi.org/10.1007/s00373-018-1957-x

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  • DOI: https://doi.org/10.1007/s00373-018-1957-x

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