Complete n- Domination Number of Union of n Copies of Certain Edge Deleted Subgraphs

Author:
1A. NELLAI MURUGAN and 2G. VICTOR EMMANUEL
Affiliation:

1Assoc. Prof. of Mathematics,V.O. Chidambaram College, Thoothukudi-628 008, Tamilnadu (INDIA)
2Research scholar, SS Pillai Research Centre for Mathematics, VOC College, Thoothukudi-628 008,Tamilnadu (INDIA)
Email: vvj_s18@yahoo.com    Email: anellai.vocc@gmail.com

Keyword:
Domination number, complete domination number, complete n-domination number. Mathematics Subject Classification: 05C69
Issue Date:
August 2014
Abstract:

The concept of complete graphs with real life application was introduced14,17. A. Nellai Murugan et. al., was introduced the concept of complete dominating number of a graph. In this paper, We introduce a new domination parameter called complete n-domination number of the union of n copies of certain edge deleted subgraphs of K4 with
edges in common , That is n images of complete graphs with edges in common. A subset S of V of a non trivial graph G is called a dominating set of G if every vertex in V-S is adjacent to at least one vertex in S. The domination number (G) of G is the minimum cardinality taken over all dominating set in G. A subset S of V of a nontrivial graph G is said to be complete dominating set, If Choose vV(G) and put S ={v}; For every v we have NG(S) = V- S denoted by S’ is the complete dominating set. The minimum cardinality taken over all complete dominating set is called the complete domination number and is denoted by n(G)14. A subset S of V of a nontrivial graph G is said to be complete n-domination number if every vertex in V is dominated by exactly n vertices of S and complete. The minimum cardinality of a complete n-dominating set is the complete n-domination number of G is denoted by nn(G). We determine this number for some standard graphs and obtain bounds for general graphs. Its relationship with other graph theoretical parameters are also investigated.

Pages:
ISSN:
2319-8052 (Online) - 2231-3478 (Print)
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Copy the following to cite this article:

1A. NELLAI MURUGAN and 2G. VICTOR EMMANUEL, "Complete n- Domination Number of Union of n Copies of Certain Edge Deleted Subgraphs", Journal of Ultra Scientist of Physical Sciences, Volume 26, Issue 2, Page Number , 2016

Copy the following to cite this URL:

1A. NELLAI MURUGAN and 2G. VICTOR EMMANUEL, "Complete n- Domination Number of Union of n Copies of Certain Edge Deleted Subgraphs", Journal of Ultra Scientist of Physical Sciences, Volume 26, Issue 2, Page Number , 2016

Available from: http://ultraphysicalsciences.org/paper/379/

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