Title of article
New results on upper domatic number of graphs
Author/Authors
Samuel, Libin Chacko Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, INDIA , Joseph, Mayamma Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, INDIA
Pages
13
From page
125
To page
137
Abstract
For a graph G = (V;E), a partition π = fV1; V2; : : : ; Vkg of the vertex set
V is an upper domatic partition if Vi dominates Vj or Vj dominates Vi or both for every
Vi; Vj 2 , whenever i 6= j. The upper domatic number D(G) is the maximum order
of an upper domatic partition of G. We study the properties of upper domatic number
and propose an upper bound in terms of clique number. Further, we discuss the upper
domatic number of certain graph classes including unicyclic graphs and power graphs
of paths and cycles.
Keywords
transitivity , upper domatic number , upper domatic partition , Domination
Journal title
Communications in Combinatorics and Optimization
Serial Year
2020
Record number
2703570
Link To Document