Bounds on Co-Secure Domination in Graphs

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2018 by IJMTT Journal
Volume-55 Number-2
Year of Publication : 2018
Authors : Aleena Joseph, V.Sangeetha
  10.14445/22315373/IJMTT-V55P520

MLA

Aleena Joseph, V.Sangeetha "Bounds on Co-Secure Domination in Graphs", International Journal of Mathematics Trends and Technology (IJMTT). V55(2):158-164 March 2018. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
Let G = (V, E) be a graph and let S⊆V. The set S is a co-secure dominating set (CSDS) of a graph G if S is a dominating set, and for each u ∈S there exists a vertex v ∈ V \ S such that uv ∈E(G) and (S \ {u})∪ {v} is adominating set.

Reference
[1] A. P. Burger, M. A. Henning and J. H. van Vuuren, “Vertex covers and secure domination in graphs”, Quaest. Math.,vol.31,pp.163-171, 2008.
[2] D.A.Mojdeh and A. N.Ghameshlou, “Domination in Jahangir Graph, J2m”, Int.J.Contemp.Math. Sciences, vol.2, pp.1193-1199, 2007.
[3] E. J. Cockayne, P. J.P. Grobler,et.at “Protection of a graph”, Util. Math., vol.67, pp.19-32, 2005.
[4] S. Arumugan,KaramEbadi and Martin Manrique “Co-Secure and Secure Domination in Graphs”, Util. Math., vol.94, pp.167-182, 2014.
[5] Zepeng Li, Zehui Shao and Jin Xu “On secure domination in trees”, Quaest. Math., vol.40, pp.1-12, 2017.

Keywords
Co-secure domination, Securedomination, Jahangir graphs, Friendship graphs, Helm graph.