Complementary Non-negative Signed Domination Number

S.Anandha Prabhavathy

doi:https://doi.org/10.14445/22315373/IJMTT-V66I5P502

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 5 | Year 2020 | Article Id. IJMTT-V66I5P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I5P502

Complementary Non-negative Signed Domination Number

S.Anandha Prabhavathy

Abstract

A function f:V->{-1,+1} is called a complementary Non-negative Signed Dominating Function (CNSDF) of G if ΣuεN[v]f(u)≥0 for every v ε V(G) with deg v≠ n-1. The Complementary Non-negative signed Domination Number of G is denoted by γCNN(G) and is defined as γCNN(G) = min{ w(f) | f is a minimal CNSDF of G }. In this paper, we initiate the study of complementary Non-negative Signed Domination number in graphs.

Keywords

Complementary Non-negative signed dominating function, Complementary Non-negative signed Domination number.

References

[1] G. Chartrand and Lesniak, Graphs and Digraphs, Fourth edition, CRC press, Boca Raton, 2005.
[2] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics,Marcel Dekker, New York(1998).
[3] T.S. Holm, On majority domination in graph, Discrete Mathematics 239(2001), 1-12.
[4] Hua-ming xing, Langfang, Liang sun, Beijing, Xue-gang chen and Taian, On signed majority total domination in graphs, Czechoslovak Mathematical Journal, 55(130)(2005), 341-348.
[5] Zhongsheng Huang, Wensheng Li, Zhifang Feng and Huaming Xing, On nonnegative signed domination in graphs, Journal of networks, Vol 8, No. 2(2013), pp, 365-372.
[6] Y.S Irine Sheela and R.Kala, Complementary Signed Dominating Functions In Graphs, Int. J. Contemp. Math. Sciences, Vol. 6,(2011),1861-1870.

Citation :

S.Anandha Prabhavathy, "Complementary Non-negative Signed Domination Number," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 5, pp. 6-11, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I5P502