Summary: Radio labelling problem of graphs have their roots in communication problem known as Channel Assignment Problem. For a simple connected graph \(G=(V(G),E(G))\), a radio labeling is a mapping \(f:V(G)\to \{0,1,2,\dots\}\) such that \(|f(u)-f(v)|\ge\text{diam}(G)+1-d(u,v)\) for each pair of distinct vertices \(u,v\in V(G)\), where \(\text{diam}(G)\) is the diameter of \(G\) and \(d(u,v)\) is the distance between \(u\) and \(v\). A radio labeling \(f\) of a graph \(G\) is a radio graceful labeling of \(G\) if \(f(V(G))=\{0,1,\dots,|V(G)|-1\}\). A graph for which a radio graceful labeling exists is called radio graceful. In this article, we study radio graceful labeling for general graphs in terms of some new parameters.