Inverse Domination And Inverse Total
Domination In Digraph

C. Kaleeswari; Dr. K. Sathya

doi:https://doi.org/10.14445/22315373/IJMTT-V66I3P503

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 3 | Year 2020 | Article Id. IJMTT-V66I3P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I3P503

Inverse Domination And Inverse Total Domination In Digraph

C. Kaleeswari, Dr. K. Sathya

Abstract

In this paper, we discussed about the various properties like domination in graph , Inverse domination in graph, Inverse total domination in graph, domination in digraph. Domination in graphs has been studied extensively. In contrast, there has been relatively little research involving domination in digraphs. In a digraph D, a vertex v openly (or 1-step) out-dominates every vertex to which v is adjacent and openly indominates every vertex from which v is adjacent. Let be a digraph. A subset S of V is called a dominating set of if for every vertex in there exists a vertex in such that . A subset S of is called a total dominating set of if is a dominating set of and the induced sub digraph has no isolated vertices. The inverse domination number g'(G) of G is the order of a smallest inverse dominating set of G. The exact values of g'(G) for some standard graphs and also establish some general results on parameter. The study of inverse total domination in graphs and present some bounds and some exact values for Also, some relationships between for and other domination parameters are established. The inverse domination parameters corresponding to domination and total domination in digraphs and establish some results on these parameters. Also we introduce the disjoint domination parameters corresponding to domination and total domination in digraphs.

Keywords

domination in graph , Inverse domination in graph, Inverse total domination in graph, domination in digraph, total domination in digraphs.

References

[1] Arumugam, .S, Jacob .K and Volkmann L., “Total and connected domination in digraphs”, Australasian J. Combin., 2007, 39, 283-292.
[2] Chartand . G and Lesniak L., “Graphs and Digraphs”, CRC, 2004.
[3] Kulli. V. R. and Janakiram B., “The dominating graph,” Graph Theory Notes of New York XLVI, 2004, 5-8.
[4] Kulli. V. R and Janakiram. B. “The Minimal Dominating Graph”, Graph Theory Notes of New York, XXVII:3, New York Academy of Sciences, 1995, 12-15.
[5] Meera Paulson and Lilly T.I., “Domination in Graph Theory” ISSN 2319-5770, e- ISSN 2394-1138, VISTAS, 2015 Vol. 4, 70-73.
[6] Kulli V. R and Radha Rajamani Iyer, “Inverse total domination in graphs ” Journal of Discrete Mathematical Sciences and Cryptography, 2007, 613-619.
[7] Kulli V. R and Sigarkanti S.C.,“Inverse domination in graphs”,Nat. Acad.Sci.Lett., 1991, Vol 14, 473-475.
[8] Kulli V. R and Patwari D.K.,“The Total Bondage Number of a Graph” in Advances in Graph Theory, 1991, 227-235.
[9] Kulli V. R., “Inverse Domination and Inverse total domination in Digraphs ”, Journal of Advanced Research in Computer Science & Technology International, 2004, Vol 2, 106-109.
[10] Kulli V. R. and Iyer R.R., “Inverse total domination in graphs”, J. Discrete Mathematical Sciences and Cryptography, 2007, 10(5), 613-62. Lee L., “On the Domination Number of a Digraph”, Ph.D. Dissertation, Michigan State University, 1994.
[11] Lisa Hansen , “Domination in Digraphs”, Western Michigan University, 1997, Vol.6.

Citation :

C. Kaleeswari, Dr. K. Sathya, "Inverse Domination And Inverse Total Domination In Digraph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 3, pp. 12-17, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I3P503