Dr. K. N. Meera

A Radio Mean labeling of a simple, finite, undirected and connected graph G is a one to one map f:V(G) → N such that for two distinct vertices u and v of $G,d(u,v)+\left|\frac{f(u)+f(v)}{2}\right|\ge 1+diam\,(G)$. The radio mean number of f, rmn(f), is the highest number assigned to any vertex of G. The radio mean number of G,rmn(G), is the minimum value of rmn(f), taken over all radio mean labelings of G. If rmn(G) = |V(G)|, we call such graphs as radio mea graceful. In this paper, we find the radio mean number of subdivision graph of complete graphs, Mongolian tent graphs, subdivision of friendship graphs and Diamond graphs and prove that these graphs are radio mean graceful.

Let G be a simple connected graph. A vertex v of G is said to be a boundary vertex of another vertex u of G if d(w, u) ≤ d(u, v) for each neighbor w of v. If a vertex v is a boundary vertex of any vertex u of G, then it is said to be a boundary vertex of the graph G. In this paper, we define a vertex v of G to be a strict boundary vertex of
another vertex u of G if d(w, u) < d(u, v) for each neighbor w of v. If a vertex v is a strict boundary vertex of any vertex u of G, then it is said to be a strict boundary vertex of the graph G. In this paper, we study the properties of strict boundary vertices of a graph.