Czechoslovak Mathematical Journal

, Volume 67, Issue 2, pp 533–536

A note on the independent domination number versus the domination number in bipartite graphs

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Abstract

Let γ(G) and i(G) be the domination number and the independent domination number of G, respectively. Rad and Volkmann posted a conjecture that i(G)/γ(G) ≤ Δ(G)/2 for any graph G, where Δ(G) is its maximum degree (see N. J. Rad, L. Volkmann (2013)). In this work, we verify the conjecture for bipartite graphs. Several graph classes attaining the extremal bound and graphs containing odd cycles with the ratio larger than Δ(G)/2 are provided as well.

Keywords

domination independent domination 

MSC 2010

05C05 05C69 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.Department of MathematicsThe University of MississippiOxfordUSA
  2. 2.Department of Mathematics and Computer ScienceAdelphi UniversityGarden CityUSA

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