Research Article

Inverse Independence Number of a Graph

by  P. G. Bhat, Surekha R Bhat
journal cover
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 42 - Issue 5
Published: March 2012
Authors: P. G. Bhat, Surekha R Bhat
10.5120/5688-7734
PDF

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 },
                        year    = { 2012 },
                        volume  = { 42 },
                        number  = { 5 },
                        pages   = { 9-13 },
                        doi     = { 10.5120/5688-7734 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }
                        %0 Journal Article
                        %D 2012
                        %A P. G. Bhat
                        %A Surekha R Bhat
                        %T Inverse Independence Number of a Graph%T 
                        %J International Journal of Computer Applications
                        %V 42
                        %N 5
                        %P 9-13
                        %R 10.5120/5688-7734
                        %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
  • 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
Computer Science
Information Sciences
No index terms available.
Keywords

Inverse Domination Number Independence Number And Inverse Independence Number

Powered by PhDFocusTM