CFP last date
20 November 2025
Call for Paper
December Edition
IJCA solicits high quality original research papers for the upcoming December edition of the journal. The last date of research paper submission is 20 November 2025

Submit your paper
Know more
The week's pick
Responsive image
A Hybrid Transformer-CNN Framework with Early and Late Fusion for Robust Skin Lesion Classification

Raihan Tanvir
Random Articles
Reseach Article

Article:The Inverse Split and Non-split Domination in Graphs

by K. Ameenal Bibi, R.Selvakumar
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 8 - Number 7
Year of Publication: 2010
Authors: K. Ameenal Bibi, R.Selvakumar
10.5120/1221-1768

K. Ameenal Bibi, R.Selvakumar . Article:The Inverse Split and Non-split Domination in Graphs. International Journal of Computer Applications. 8, 7 ( October 2010), 21-29. DOI=10.5120/1221-1768

@article{ 10.5120/1221-1768,
author = { K. Ameenal Bibi, R.Selvakumar },
title = { Article:The Inverse Split and Non-split Domination in Graphs },
journal = { International Journal of Computer Applications },
issue_date = { October 2010 },
volume = { 8 },
number = { 7 },
month = { October },
year = { 2010 },
issn = { 0975-8887 },
pages = { 21-29 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume8/number7/1221-1768/ },
doi = { 10.5120/1221-1768 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T19:56:50.360368+05:30
%A K. Ameenal Bibi
%A R.Selvakumar
%T Article:The Inverse Split and Non-split Domination in Graphs
%J International Journal of Computer Applications
%@ 0975-8887
%V 8
%N 7
%P 21-29
%D 2010
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, we define the notions of inverse split and non split domination in graphs. We get many bounds on inverse split and non split domination numbers. Nordhaus-Gaddum type results are also obtained for these new parameters.

References
  1. 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 – 600 034. July 25-26.
  2. Ameenal Bibi, K. and Selvakumar, R (2009). The Inverse strong non-split r-domination number of a graph. Proc. of the National Conference on Industrial Applications of Mathematics, NCMA 2009, PG and Research Dept. of Mathematics, Sacred Heart College (Autonomous) Tirupattur, Vellore Dist., March 12-13.
  3. Ameenal Bibi, K. and Selvakumar, R (2010). The inverse strong non-split r-domination number of a graph – International Journal of Engineering, science and Technology, Vol.2, No. 1, pp. 127-133.; www.ijest_ng.com, ISSN No. for IJEST: For printed version : 2141-2820 For online version : 2141-2839.
  4. Arumugam, S. and Velammal, S. (1998). Edge domination in graphs, Taiwanese Journal of Mathematics, Vol. 2, No. 2, pp. 173-179.
  5. Chartrand G. and Lesniak L. (1996). Graphs and Digraphs. Chapman and Hall / CRC.
  6. Chartrand G. and Schuster S. (1974). On the independence number of complementary graphs. Trans. of the New York Acad. of Sci. Series II, 36 No. 3 pp. 247-251.
  7. Cockayne, E.J. and Hedetniemi S.T. (1977). Towards a theory of domination in graphs. Networks, 7. pp. 241-267.
  8. Cockayne, E.J., Dawes R.M. and Hedetniemi S.T. (1980). Total domination in Graphs. Networks, Vol. 10. pp. 211-219.
  9. Domke G.S., Dunbar J.E. and Markus L.R (2007). The Inverse domination number of a graph, Feb’ (2007).
  10. Haynes, T.W., Hedetniemi S.T. and Slater P.J. (1998). Domination in Graphs : Advanced Topics, Marcel Dekker Inc. New York, U.S.A.
  11. Haynes, T.W., Hedetniemi S.T. and Slater P.J. (1998). Fundamentals of domination in graphs, Marcel Dekker Inc. New York, U.S.A.
  12. Jayaram, S.R. (1987). Graphs and Combinatorics 3 pp. 357-363.
  13. Joseph A.Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics 15, 2008.
  14. Kulli, V.R. and Sigarkanti, S.C. (1988). The connected edge domination number of a graph. Proc. R.C. Bose Mem. Conf. Abstract.
  15. Kulli, V.R. and Janakiram B. (1997). The split domination number of a graph. Graph Theory notes of New York. Newyork Academy of Sciences, XXXII. pp. 16-19.
  16. Kulli, V.R. and Janakiram B. (2000). The non-split domination number of a graph. The Journal of Pure and Applied Math. 31(5). pp. 545-550.
  17. Kulli, V.R. and Janakiram B. (2003). The strong non-split domination number of a graph. International Journal of Management and Systems. Vol. 19, No. 2, pp. 145-156.
  18. Kulli, V.R. and Sigarkanti S.C. (1991). Inverse domination in graphs. National Academy Science Letters, 15.
  19. Kulli, V.R., Janakiram B. and Radha Iyer R. (1999). The Cototal domination number of a graph. Journal of Discrete Mathematical Sciences and Cryptography. Vol. 2 pp. 179-185.
  20. Mitchell, S. and Hedetniemi, S.T. (1977). Edge domination in trees, Congr.Numer., pp. 489-509, 1977.
  21. Nordhaus, E.A. and Gaddum J.W. (1956). On complementary graphs. Amer.Math.Monthly, 63. pp. 175-177.
  22. Ore, O. (1962). Theory of Graphs. American Mathematical Society Colloq. Publ., Providence, RI, 38.
Index Terms

Computer Science
Information Sciences

Keywords

Independent set dominating set split dominating set non-split dominating set inverse split dominating set inverse non-split dominating set inverse split and non-split domination numbers

Powered by PhDFocusTM