Bounds on Co-Independent Liar’s Domination in Graphs

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, NGv∩S≥2, (ii) for every pair u,v∈V of distinct vertices, NGu∪NGv∩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 γcoiLRG. 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.