The week's pick
Random Articles
Reseach Article
Inverse Independence Number of a Graph
| 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
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
- Ameenal Bibi K. , Selvakumar R. , The Inverse Split and Non-split Domination in Graphs, IJCA Vol. 8– No. 7, ( 2010), 21-29.
- Ameenal Bibi K, Selvakumar R, The Inverse Domination in Semitotal Block Graphs, IJCA Vol. 8– No. 8, ( 2010), 4-7.
- Domke G. S, Dunbar J. E. and Lisa S Markus, Inverse Dominating sets, Ars Combinatoria, Vol. 72 (2004) , 113-118.
- Frucht R and Harary F. , On Corona of two graphs, Aequationes Math. ,4(1970), 322- 324.
- Harary F. , Graph Theory, Addison Wiley, 1969.
- Haynes T. W. , Hedetniemi S. T. , Slater P. J. , Fundamentals of Domination in Graphs, Marcel Dekker, Inc. , N. Y. , 1998.
- 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.
- Kamath S. S. and Bhat R. S. , On strong (weak) independence number and vertex coverings of a graph, Discrete Mathematics, 307,(2007) 1136 – 1145.
- Kulli V. R. and Sigarakanti S. C. , Inverse Domination in Graphs, National Academy science letters, 14 (1991),473-475.
- Tamizh Chelvam T and Grace Prema G. S. , Equality of Domination and Inverse Domination, ARS Combinatoria, 95(2010), 103-111
Index Terms
Keywords