Bounds on Co-Independent Liar's Domination in Graphs


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Prabha K. S. , Amutha S., Anbazhagan N., Cangül İ. N.

JOURNAL OF MATHEMATICS, vol.2021, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2021
  • Publication Date: 2021
  • Doi Number: 10.1155/2021/5544559
  • Title of Journal : JOURNAL OF MATHEMATICS

Abstract

A set S subset of V of a graph G = (V, E) is called a co-independent liar's dominating set of G if (i) for all v is an element of V, vertical bar N-G[v] boolean AND S vertical bar >= 2, (ii) for every pair u, v is an element of V of distinct vertices, vertical bar N-G[u] boolean OR N-G [v]) boolean AND S vertical bar >= 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 gamma(LR)(coi) (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.