Let $\gamma(G)$ and $i(G)$ be the domination number and the independentdomination number of $G$, respectively. Rad and Volkmann posted a conjecturethat $i(G)/ \gamma(G) \leq \Delta(G)/2$ for any graph $G$, where $\Delta(G)$ isits maximum degree (See \cite{5}: N.J. Rad, L. Volkmann, A note on theindependent domination number in graphs. Discrete Appl. Math. 161(2013)3087--3089). In this work, we verify the conjecture for bipartite graphs.Several graph classes attaining the extremal bound and graphs containing oddcycles with the ratio larger than $\Delta(G)/2$ are provided as well.
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