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IJSTR >> Volume 4 - Issue 12, December 2015 Edition



International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616



Generalized 2-Complement Of Set Domination

[Full Text]

 

AUTHOR(S)

P. Sumathi, T. Brindha

 

KEYWORDS

Key words: Dominating set, set dominating set, 2-complement of G.

 

ABSTRACT

Abstract: Let G=(V,E) be a simple, undirected, finite nontrivial graph. A set SÍV of vertices of a graph G = (V, E) is called a dominating set if every vertex vÎV is either an element of S or is adjacent to an element of S. A set SÍV is a set dominating set if for every set TÍV-S , there exists a non-empty set RÍS such that the subgraph is connected. The minimum cardinality of a set dominating set is called set domination number and it is denoted by γs (G).Let P=(V1,V2) be a partition of V,from E(G) remove the edges between V1 and V2 in G and join the edges between V1 and V2 which are not in G. The graph G2p thus obtained is called 2-complement of G with respect to ‘P’.

 

REFERENCES

[1] Hedetniemi. S.C., and Laskar,”Topics on Domination” Annals of Discrete Mathematics., 48., North Holland(1991)

[2] Teresa W. Haynes, Stephen T. Hedetniemi, Peter J. Slater. “Fundamentals of Domination in Graphs”, Marcel Dekker, Inc.,(1998).

[3] E. Sampath kumar and pushpalatha, ”complement of a graph : A generalization Graphs and combinatories” (1998)

[4] E. Sampathkumar and L. pushpalatha, “Generalized complement of a graph, Indian journal of Pure and Applied Mathematics “June(1999).