Upper Domatic Number of Certain Graphs

Abstract

Let be a graph with vertex set  and edge set . The maximum order of the partitions of the vertex set represented by , is called upper domatic number where each class of partition dominates one another (i.e.) dominates  or  dominates  or both . Upper domatic number is denoted by . In this paper we determine the upper domatic number of certain graphs such as double fan graph DF_n, friendship graph F_n and helm graph H_n.