2016/03/24 by Lang Tang, Tang, Lang, Shenglin Zhou +1
Computer Science · Mathematics · #05B05 #05C69 #05E18 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1603.07398
openalex publication_date 2016/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G=(V,E) be a simple connected graph. A set of vertices S⊆ V is said to be a dominating set if for any vertex in V∖ S is adjacent to at least one vertex in S. The domination number γ(G) of G is the minimum cardinality among all such sets. In this paper, we obtain some results on the domination number of the incidence graphs of combinatorial designs. In particular, we prove a conjecture and disprove another conjecture in a recent paper by Goldberg, Rajendraprasad and Mathew. We also prove a third conjecture by the same authors for block-transitive symmetric designs.