Affiliation:
1. Department of Mathematics, Thiagarajar College of Engineering, Madurai 625 015, India
2. Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Kalavakkam, Chennai 603 110, India
3. Ramanujan Research Center in Mathematics, Saraswathi Narayanan College, Madurai 625 022, India
Abstract
In secure domination [A. P. Burger, M. A. Henning and J. H. Van Vuuren, Vertex covers and secure domination in graphs, Quaest Math. 31 (2008) 163–171; E. J. Cockayne, Irredundance, secure domination and maximum degree in trees, Discrete Math. 307(1) (2007) 12–17; E. J. Cockayne, O. Favaron and C. M. Mynhardt, Secure domination, weak Roman domination and forbidden subgraph, Bull. Inst. Combin. Appl. 39 (2003) 87–100; C. M. Mynhardt, H. C. Swart and E. Ungerer, Excellent trees and secure domination, Util. Math. 67 (2005) 255–267], a vertex outside has the chance of coming inside the dominating set by replacing an element of the set without affecting domination. This idea is combined with equitability. Secure equitable dominating set is introduced and studied. Other concepts like independence and rigid security are also studied in this paper.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Discrete Mathematics and Combinatorics