A Study on Total Rebellion Number in Graphs (Journal of Informatics and Mathematical Sciences, 2017)
A set $R\subseteq V$ of a graph \(G = (V,E)\) is said to be a `rebellion set' (\(rb\)-set) of \(G\), if \(\arrowvert N_R(v) \arrowvert ≤ \arrowvert N_{V/R}(v) \arrowvert\), for all \(v\in R\), \(\arrowvert R\arrowvert ≥ \arrowvert V/R \arrowvert\) and \(\la R\ra\) 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.
Keywords: Rebellion number and Total rebellion number