Relationship of global connected domination number and colouring parameter of a graph

Graph theory has got rich in applications in Computer science and Engineering, especially the theory of domination in graphs. Many new types of domination parameters has got its own applications. A dominating set S⊆V for a graph G is such that each v∈V is either in S or adjacent to a node of D. The domination number γ(G) is the minimum cardinality of a dominating set of G. A dominating set S of a connected graph G is called a connected dominating set if <; S > is connected. A set S is called a global dominating set of G if S is a dominating set of both G and G̅. A subset S of nodes of a graph G is called a global connected dominating set if S is both a global dominating and a connected dominating set. The global connected domination number is the minimum cardinality of a global connected dominating set of G and is denoted by γ
_gc
(G). In [3], we have already exhibited all graphs their sum of global connected domination number and chromatic number of order upto 2p-5. Since, graph coloring especially chromatic number of a graph has variety of applications, in this paper, we exhibit all graphs their sum of γ
_gc
-number and chromatic number equals to 2p-6 for p > 3.