2015/12/15 by Akbari, Saieed, Motiei, Mohammad, Mozaffari, Sahand +1
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.1512.04748
Let G be a graph. A total dominating set of G is a set S of vertices of G such that every vertex is adjacent to at least one vertex in S. The total domatic number of a graph is the maximum number of total dominating sets which partition the vertex set of G. In this paper we would like to characterize the cubic graphs with total domatic number at least two.