2023/02/27 by Ghanbari, Nima, Alikhani, Saeid
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2302.14129
A set D of vertices of a simple graph G=(V,E) is a strong dominating set, if for every vertex x∈ D=V∖ D there is a vertex y∈ D with xy∈ E(G) and deg(x)≤ deg(y). The strong domination number γst(G) is defined as the minimum cardinality of a strong dominating set. The strong domatic number of G is the maximum number of strong dominating sets into which the vertex set of G can be partitioned. We initiate the study of the strong domatic number, and we present different sharp bounds on dst(G). In addition, we determine this parameter for some classes of graphs, such as cubic graphs of order at most 10.