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An Improved Upper Bound on the Independent Domination Number in Cubic Graphs of Girth at Least Six

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Abstract

Henning et al. (Discrete Appl Math 162:399–403, 2014) proved that if G is a bipartite, cubic graph of order n and of girth at least 6, then \(i(G) \le \frac{4}{11}n\). In this paper, we improve the \(\frac{4}{11}\)-bound to a \(\frac{5}{14}\)-bound, and prove that if G is a bipartite, cubic graph of order n and of girth at least 6, then \(i(G) \le \frac{5}{14}n\).

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad, 91775, Iran

    Gholamreza Abrishami

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

    Michael A. Henning

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  1. Gholamreza Abrishami
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  2. Michael A. Henning
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Correspondence to Michael A. Henning.

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Research supported in part by the University of Johannesburg.

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Abrishami, G., Henning, M.A. An Improved Upper Bound on the Independent Domination Number in Cubic Graphs of Girth at Least Six. Graphs and Combinatorics 38, 50 (2022). https://doi.org/10.1007/s00373-021-02446-y

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  • DOI: https://doi.org/10.1007/s00373-021-02446-y

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