A note on the independent domination number versus the domination number in bipartite graphs
Shaohui Wang, Bing Wei · Czechoslovak Mathematical Journal · 2017
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) ∆(G)/2 for any graph G, where ∆(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 ∆(G)/2 are provided as well.