Minimal dominating sets in maximum domatic partitions.
S. Arumugam, Kameshwar Chandrasekar · Australas. J Comb. · 2012
The domatic number d(G) of a graph G = (V,E) is the maximum order of a partition of V into dominating sets. Such a partition Π = {D1, D2, . . . , Dd} is called a minimal dominating d-partition if Π contains the maximum number of minimal dominating sets, where the maximum is taken over all d-partitions of G. The minimal dominating d-partition number Λ(G) is the number of minimal dominating sets in a minimal dominating d-partition of G. In this paper we initiate a study of this parameter.