2025/04/09 by Henning, Michael A., Maniya, Paras Vinubhai, Pradhan, Dinabandhu
#05C69 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.2504.07186
A disjunctive dominating set of a graph G is a set D ⊆ V(G) such that every vertex in V(G)∖ D has a neighbor in D or has at least two vertices in D at distance 2 from it. The disjunctive domination number of G, denoted by γ2d(G), is the minimum cardinality of a disjunctive dominating set of G. In this paper, we show that if G is a maximal outerplanar graph of order n ≥ 7 with k vertices of degree 2, then γ2d(G)≤ \lfloor(2)/(9)(n+k)\rfloor, and this bound is sharp.