In this paper, we determine for a simple graph G on n vertices and m edges a variety of domination parameters such as connected domination number, outer connected domination number, doubly connected domination number, global domination number, total global connected domination number, 2-connected domination number, strong domination number, fair domination number, independence domination number etc.

The concept of vertex coloring pose a number of challenging open problems in graph theory. Among several interesting parameters, the coloring parameter, namely the pseudoachromatic number of a graph stands a class apart. Although not studied very widely like other parameters in the graph coloring literature, it has started gaining prominence in recent years. The pseudoachromatic number of a simple graph G, denoted ψ(G), is the maximum number of colors used in a vertex coloring of G, where the adjacent vertices may or may not receive the same color but any two distinct pair of colors are represented by at least one edge in it. In this paper we have computed this parameter for a number of classes of graphs.

In this paper, we compute various Domination numbers like Outer Connected Domination (OCD), Doubly Connected Domination (DCD), Fair Domination (FD), Independence Domination (ID), 2-Packing (2-P) for Rolf Nevanlinna Prize Winners's Collaboration Graph (RNPCG).