Changing and Unchanging of Minus Domination in Graphs

Poorvi A. G; V.Sangeetha

doi:https://doi.org/10.14445/22315373/IJMTT-V55P526

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 55 | Number 3 | Year 2018 | Article Id. IJMTT-V55P526 | DOI : https://doi.org/10.14445/22315373/IJMTT-V55P526

Changing and Unchanging of Minus Domination in Graphs

Poorvi A. G, V.Sangeetha

Citation :

Poorvi A. G, V.Sangeetha, "Changing and Unchanging of Minus Domination in Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 55, no. 3, pp. 200-211, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V55P526

Abstract

A function f V G : ( ) { 1, 0,1}   defined on the vertex set of a graph G V E  ( , ) is said to be a minus dominating function if the sum of its function values over every closed neighbourhood is at least one. That is for every v V f N v   , ( [ ]) 1 , where N v( ) consists of v and every vertex adjacent to v. The weight of a minus dominating function is f V f v ( ) ( )  , over all vertices v V . The minus domination number of a graph G , denoted by  ( ) G  is equal to the minimum weight of a minus domination function of G . In this paper, we study the change in minus domination number after adding an edge to paths and 1 , 3 n C K n  B. We also investigate the bounds for minus domination number of Jahangir graph and the line graph of sun let graphs.

Keywords

Jahangir graph, sunlet graph, line graph, corona graph.

References

[1] J. Dunbar, S. Hedetniemi, M. A. Henning, A. McRae, “Minus domination in graphs”, Discrete Mathematics, vol. 199, pp. 35-47, 1999.
[2] D. A. Mojdeh, A. N. Ghameshlou, “Domination in Jahangir Graph 2 ,m J ”, Int. J. Contemp. Math. Sciences, vol. 2, no. 24, pp. 1193- 1199,2007.
[3] H. M. Xing, Tianjin, H. L. Liu, “Minus total domination in graphs”, Czechoslovak Mathematical Journal, vol. 59, pp. 861-870, 2009.
[4] C. E. Go, S. R. Canoy, “Domination in corona and join of graphs”, International Mathematical Forum, vol. 6, no. 16, pp. 763-771, 2011.
[5] L. Kang, H. K. Kim, M. Y. Sohn, “Minus total domination in k-partite graphs”, Discrete Mathematics, vol. 227, pp. 295-300, 2004.