Results on Split, Non-Split, Inverse Split and Inverse Non-Split Domination Number of Some Special Graphs

T.Aswini; Dr. K.Ameenal Bibi

doi:https://doi.org/10.14445/22315373/IJMTT-V66I8P505

International Journal of Mathematics Trends and Technology

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Volume 66 | Issue 8 | Year 2020 | Article Id. IJMTT-V66I8P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I8P505

Results on Split, Non-Split, Inverse Split and Inverse Non-Split Domination Number of Some Special Graphs

T.Aswini, Dr. K.Ameenal Bibi

Abstract

Let G=(V,E) be a simple, finite, connected and indirected graph. A non-empty subset D ⊆ V is called a dominating set if every vertex in V-D adjacent to at least one vertex in D. The minimum cardinality taken over all the minimal dominating sets of G is called the domination number of G, denoted by γ(G). Let G be the minimum dominating set of G. If V-D contains a dominating set D is called the inverse dominating set of G with respect to D. The inverse dominating number γ'(G) is the minimum cardinality taken over all the minimal inverse dominating set of G. A dominating set D ⊆ V of a graph G is a split(non-split) dominating set if the induced sub graph is disconnected(connected). The split ( not-split) domination number γs(G)[γms(G)] is the minimum cardinality of a split(non-split) dominating set.

Keywords

Dominating set, inverse dominating set, split and non-split domination number, inverse split domination number and inverse non-split domination number.

References

[1] T. W. Haynes, S.T. Hedetriemi and P. J. Slater, “fundamentals of domination in graphs” Marcel Dekkar, New York(1990).
[2] V.R. Kulli and B. Janakiram, “The non-split domination number of a graph, Indian Journal of pure and applied mathematics (1996) 27(6), 537-542.
[3] O. Ore, Theory of Graphs, American math colloq (1962).
[4] Ameenal Bibi. K and Selvakumar. R(2008). “The inverse split and non-split domination numbers in graphs”. Proc. of the international conference on mathematics and computer science, ICMCS 2008, Dept. of mathematics, Loyola College, Chennai- 600034,
[5] Domke G. S. Dunbar J. E. and Markus L. R (2007). “The inverse domination in graphs”, Feb (2007).
[6] Harary F, Graph theory, Addition-Wesley, Reading mass, 1969.
[7] S.Arumugam and S. Ramachandran, “Invitation of Graph Theory”, Scitech publications, India (2010).
[8] Bordy J and Murthy V.S.R Graph Theory with Applications Mac Millan Press London (1976)
[9] V.R. Kulli, College Graph Theory, Vishwa International publications, Gulbarga, Indian (2012)
[10] T.W. Hynes, S.T. Hedetriemi and P.J. Slater, Domination in Graphs: Advanced Topics: Marcel Dekkar, New York (1998).

Citation :

T.Aswini, Dr. K.Ameenal Bibi, "Results on Split, Non-Split, Inverse Split and Inverse Non-Split Domination Number of Some Special Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 8, pp. 34-45, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I8P505