The Non-Split Complement Line Domination in Graphs

Authors

  • V. Mohanaselvi Department of Mathematics, Nehru Memorial College, Puthanampatti, Tiruchirappalli 621 007, Tamil Nadu
  • P. Kavitha Department of Mathematics, Nehru Memorial College, Puthanampatti, Tiruchirappalli 621 007, Tamil Nadu
  • M. Durka Devi Department of Mathematics, Nehru Memorial College, Puthanampatti, Tiruchirappalli 621 007, Tamil Nadu

DOI:

https://doi.org/10.26713/jims.v9i3.761

Keywords:

Graph, Line graph, Domination number, Line domination number, Split line domination number, Split complement line domination number

Abstract

Harary and Norman introduced the Line graph \(L(G)\). We introduced the split complement line domonation number by posting the disconnected property on the dominating sets of \(\overline{L(G)}\). In this paper, we study the connectedness property of dominating sets of \(\overline{L(G)}\) by defining non-split domination parameter. Also, we studied its graph theoretical properties in terms of elements of \(G\).

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References

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F. Harary, Graph Theory, Addison-Wesley Publication, Reading”Massachusetts”Menlo Park”California”London, pp. 71 – 83 (1972).

F. Harary and R.Z. Norman, Some properties of line graphs, Rendiconti del circolo mathematico di palmero 9 (2) (1960), 166 – 168.

T.W. Hayness, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs, Marcel-Dekker, Inc., New York (1998)

V.R. Kulli and B. Janakiram, The non-split domination number of graph, Indian J. Pure and Appl. Math. 31 (4) (2000), 545 – 550.

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M.H. Muddebihal, U.A. Panfarosh and Anil R. Seetamkar, Split line domination in graphs, International Journal of Science and Research 3 (8) (2014), 1163 – 1166.

O. Ore, Theory of graphs, Amer. Math. Soc. Colloq. Publ., 38, Providence (1962).

D.F. Rall, Dominating a graph and its complement, Congressus Numerantium 80 (1991), 89 – 95.

E. Sampathkumar, The global domination number of a graph, J. Math. Phys. Sci. 23 (1989), 377 – 385.

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CITATION

How to Cite

Mohanaselvi, V., Kavitha, P., & Devi, M. D. (2017). The Non-Split Complement Line Domination in Graphs. Journal of Informatics and Mathematical Sciences, 9(3), 557–570. https://doi.org/10.26713/jims.v9i3.761

Issue

Vol. 9 No. 3 (2017)

Section

Research Articles

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