A Study on Total Rebellion Number in Graphs - Mohanaselvi, V.; Mary, P. Shyamala Anto; Monisha, A. (Journal of Informatics and Mathematical Sciences, 2017)
A set RV of a graph \(G = (V,E)\) is said to be a `rebellion set’ (\(rb\)-set) of \(G\), if \(N_R(v) ≤ N_V/R(v) \), for all \(vR\), \(R≥ V/R \) and \(R a\) has no isolated vertices. The total rebellion number \(trb(G)\) is the minimum cardinality of any total rebellion set in \(G\). A total rebellion set with cardinality \(trb(G)\) is denoted by \(trb(G)\)-set. In this paper, we defined the total rebellion number for simple graphs. Also, we determined its tight bounds for some standard graph and characterize this parameters.