A note on the independent domination number versus the domination number in bipartite graphs
- First Online:
- 30 Downloads
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.
Keywordsdomination independent domination
MSC 201005C05 05C69
Unable to display preview. Download preview PDF.
- T. Beyer, A. Proskurowski, S. Hedetniemi, S. Mitchell: Independent domination in trees. Proc. Conf. on Combinatorics, Graph Theory and Computing. Baton Rouge, 1977, Congressus Numerantium, Utilitas Math., Winnipeg, 1977, pp. 321–328.Google Scholar