Title: Relationship of global connected domination number and colouring parameter of a graph
Abstract: 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gc</sub> (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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gc</sub> -number and chromatic number equals to 2p-6 for p > 3.
Publication Year: 2015
Publication Date: 2015-01-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot