EVEN RADIO MEAN GRACEFUL LABELING ON DEGREE SPLITTING OF SNAKE RELATED GRAPHS

A radio mean labeling of a connected graph G is an injection $\phi$ from the vertex set V(G) to N such that the condition $d(u, v)+ \Bigg \lceil \frac{ {\phi(u) + \phi(v)} }{ 2 }\Bigg \rceil $ $\geq 1 + diam(G)$ holds for any two distinct vertices u and v of G. A graph which admits radio mean labeling is called radio mean graph. The radio mean number of $\phi$, rmn$(\phi)$, is the maximum number assigned to any vertex of G. The radio mean number of G, rmn(G), is the minimum value of rmn$(\phi)$ taken over all radio mean labeling $\phi$ of G. In this paper we introduce a new concept even radio mean graceful labeling and we investigate the even radio mean graceful labeling on degree splitting of snake related graphs.