A Study on Total Rebellion Number in Graphs

V. Mohanaselvi, P. Shyamala Anto Mary, A. Monisha


A set $R\subseteq V$ of a graph \(G = (V,E)\) is said to be a `rebellion set' (\(rb\)-set) of \(G\), if \(\arrowvert N_R(v) \arrowvert \leq \arrowvert N_{V/R}(v) \arrowvert\), for all \(v\in R\), \(\arrowvert R\arrowvert \geq \arrowvert V/R \arrowvert\) and \(\la R\ra\) has no isolated vertices. The total rebellion number \(\mathit{trb}(G)\) is the minimum cardinality of any total rebellion set in \(G\). A total rebellion set with cardinality \(\mathit{trb}(G)\) is denoted by \(\mathit{trb}(G)\)-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.


Rebellion number and Total rebellion number

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DOI: http://dx.doi.org/10.26713%2Fjims.v9i3.938

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