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Boundary Domination of Line and Middle Graph of Wheel Graph Families

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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2016
Authors:
Mohammed Alatif, Puttaswamy Rangaiah, Nayaka S.R.
10.5120/ijca2016907928

Mohammed Alatif, Puttaswamy Rangaiah and Nayaka S.R.. Article: Boundary Domination of Line and Middle Graph of Wheel Graph Families. International Journal of Computer Applications 134(5):1-5, January 2016. Published by Foundation of Computer Science (FCS), NY, USA. BibTeX

@article{key:article,
	author = {Mohammed Alatif and Puttaswamy Rangaiah and Nayaka S.R.},
	title = {Article: Boundary Domination of Line and Middle Graph of Wheel Graph Families},
	journal = {International Journal of Computer Applications},
	year = {2016},
	volume = {134},
	number = {5},
	pages = {1-5},
	month = {January},
	note = {Published by Foundation of Computer Science (FCS), NY, USA}
}

Abstract

Let G = (V;E) be a connected graph. A subset S of V (G) is called a boundary dominating set if every vertex of V − S is boundary dominated by some vertex of S. The minimum taken over all boundary dominating sets of a graph G is called the boundary domination number of G and is denoted by γb(G). We define the boundary domatic number in graphs. Exact values of of Wheel Graph Families are obtained and some other interesting results are established.

References

  1. Ayhan A. Khalil, Determination and Testing the Domination Numbers of Helm Graph, J. Edu. and Sci, Vol. (24), No. (2) 2011.
  2. F. Buckley and F. Harary, Distance in Graphs, Addison- Wesley Reading, 1990.
  3. G. Chartrand, David Erwin, G. L. Johns and P. Zhang, On boundary vertices in graphs, J. Combin. Math. Combin. Comput., 48(2004), 39-53.
  4. T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York, (1997).
  5. KM. Kathiresan, G. Marimuthu and M. Sivanandha Saraswathy, Boundary domination in graphs, Kragujevac J. Math. 33 (2010) 63-70.
  6. Puttaswamy and Mohammed Alatif , Boundary edge domination in graphs, Bulletin Of the International Mathematical Virtual Instiute. 5(2015)197-204
  7. B. Zelinka, Edge domatic number of a graph, Czech. Math. J., 33(108)(1983), 107-110.

Keywords

Boundary dominating set, Boundary domination number, Boundary domatic number