Czechoslovak Mathematical Journal, Vol. 67, No. 2, pp. 533-536, 2017
A note on the independent domination number versus the domination number in bipartite graphs
Shaohui Wang, Bing Wei
Received February 12, 2016. First published March 1, 2017.
Abstract: Let $\gamma(G)$ and $i(G)$ be the domination number and the independent domination number of $G$, respectively. Rad and Volkmann posted a conjecture that $i(G)/ \gamma(G) \leq\Delta(G)/2$ for any graph $G$, where $\Delta(G)$ 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 $\Delta(G)/2$ are provided as well.
Affiliations: Shaohui Wang, Department of Mathematics, The University of Mississippi, University Avenue, University, Mississippi 38677, USA, and Department of Mathematics and Computer Science, Adelphi University, 1 South Ave, Garden City, New York 11530, USA, e-mail: email@example.com; Bing Wei, Department of Mathematics, The University of Mississippi, University Avenue, University, Mississippi 38677, USA, e-mail: firstname.lastname@example.org