CFP last date
20 May 2024
Call for Paper
June Edition
IJCA solicits high quality original research papers for the upcoming June edition of the journal. The last date of research paper submission is 20 May 2024

Submit your paper
Know more
The week's pick
Responsive image
Enhancing Privacy Preservation: Multi-Attribute Protection with P-Sensitive K-Anonymity

Twinkle Patel Kiran Amin
Random Articles
Reseach Article

Inverse Independence Number of a Graph

by P. G. Bhat, Surekha R Bhat
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 42 - Number 5
Year of Publication: 2012
Authors: P. G. Bhat, Surekha R Bhat
10.5120/5688-7734

P. G. Bhat, Surekha R Bhat . Inverse Independence Number of a Graph. International Journal of Computer Applications. 42, 5 ( March 2012), 9-13. DOI=10.5120/5688-7734

@article{ 10.5120/5688-7734,
author = { P. G. Bhat, Surekha R Bhat },
title = { Inverse Independence Number of a Graph },
journal = { International Journal of Computer Applications },
issue_date = { March 2012 },
volume = { 42 },
number = { 5 },
month = { March },
year = { 2012 },
issn = { 0975-8887 },
pages = { 9-13 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume42/number5/5688-7734/ },
doi = { 10.5120/5688-7734 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:30:37.062161+05:30
%A P. G. Bhat
%A Surekha R Bhat
%T Inverse Independence Number of a Graph
%J International Journal of Computer Applications
%@ 0975-8887
%V 42
%N 5
%P 9-13
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The concept of inverse domination was introduced by Kulli V. R. and Sigarakanti S. C. [9] . Let D be a ? - set of G. A dominating set D1 ? V- D is called an inverse dominating set of G with respect to D. The inverse domination number ? ? (G) is the order of a smallest inverse dominating set. Motivated by this definition we define another parameter as follows. Let D be a maximum independent set in G. An independent set S ? V- D is called an inverse independent set with respect to D. The inverse independence Number ?0-1(G) = max {|S| : S is an inverse independent set of G}. We find few bounds on inverse domination number and also initiate the study of the inverse independence number giving few bounds on inverse independence number of a graph.

References
  1. Ameenal Bibi K. , Selvakumar R. , The Inverse Split and Non-split Domination in Graphs, IJCA Vol. 8– No. 7, ( 2010), 21-29.
  2. Ameenal Bibi K, Selvakumar R, The Inverse Domination in Semitotal Block Graphs, IJCA Vol. 8– No. 8, ( 2010), 4-7.
  3. Domke G. S, Dunbar J. E. and Lisa S Markus, Inverse Dominating sets, Ars Combinatoria, Vol. 72 (2004) , 113-118.
  4. Frucht R and Harary F. , On Corona of two graphs, Aequationes Math. ,4(1970), 322- 324.
  5. Harary F. , Graph Theory, Addison Wiley, 1969.
  6. Haynes T. W. , Hedetniemi S. T. , Slater P. J. , Fundamentals of Domination in Graphs, Marcel Dekker, Inc. , N. Y. , 1998.
  7. Hedetniemi S. M. , Hedetniemi S. T, Renu C. Laskar, Slater P. J. , Disjoint dominating sets, Proceedings of Int. conf. on Disc. Math. (ICDM 2006) 88- 102.
  8. Kamath S. S. and Bhat R. S. , On strong (weak) independence number and vertex coverings of a graph, Discrete Mathematics, 307,(2007) 1136 – 1145.
  9. Kulli V. R. and Sigarakanti S. C. , Inverse Domination in Graphs, National Academy science letters, 14 (1991),473-475.
  10. Tamizh Chelvam T and Grace Prema G. S. , Equality of Domination and Inverse Domination, ARS Combinatoria, 95(2010), 103-111
Index Terms

Computer Science
Information Sciences

Keywords

Inverse Domination Number Independence Number And Inverse Independence Number

Powered by PhDFocusTM