Radio even mean graceful labeling on some special graphs

Abstract

Radio Even Mean Graceful Labeling of a connected graph \(G\) is a bijection \(\phi\) from the vertex set \(V(G)\) to \(\{2,4,6, \ldots 2|V|\}\) satisfying the condition \(d(s, t)+\left\lceil\frac{\phi(s)+\phi(t)}{2}\right\rceil \geq 1+\operatorname{diam}(G)\) for every \(\mathrm{s}, \mathrm{t} \in \mathrm{V}(\mathrm{G})\). A graph which admits radio even mean graceful labeling is called radio even mean graceful graph. In this paper we investigate the radio even mean graceful labeling on degree splitting of some special graphs.