Bounds on Co-Independent Liar's Domination in Graphs. (20th March 2021)

• Record Type: Journal Article
• Authors: Prabha, K. Suriya; Amutha, S.; Anbazhagan, N.; Cangul, Ismail Naci
• Other Names: Shabbir Ghulam Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2021(2021)
• Publication Date: 2021-03-20
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2021/5544559
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : A set S ⊆ V of a graph G = V, E is called a co-independent liar's dominating set of G if (i) for all v ∈ V, N G v ∩ S ≥ 2, (ii) for every pair u, v ∈ V of distinct vertices, N G u ∪ N G v ∩ S ≥ 3, and (iii) the induced subgraph of G on V − S has no edge. The minimum cardinality of vertices in such a set is called the co-independent liar's domination number of G, and it is denoted by γ coi L R G . In this paper, we introduce the concept of co-independent liar's domination number of the middle graph of some standard graphs such as path and cycle graphs, and we propose some bounds on this new parameter.