2016/06/17 by Shaohui Wang, Wang, Shaohui, Bing Wei +1
Computer Science · Mathematics · Neuroscience · #05C05 #05C69 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Nuclear Receptors and Signaling
paper · pdf · doi:10.48550/arxiv.1606.05599
openalex publication_date 2016/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \cite5: N.J. Rad, L. Volkmann, A note on the independent 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 odd cycles with the ratio larger than Δ(G)/2 are provided as well.