Dr. K. N. Meera

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.

Let G(V, E) be a simple, finite, connected graph. An injective mapping f : V (G) → Z + such that for every two distinct vertices u, v ∈ V (G), |f(u) − f(v)| ≥ diam(G) + 1 − d(u, v) is called a radio labeling of G. The radio number of f, denoted by rn(f) is the maximum number assigned to any vertex of G. The radio number of G, is the minimum value of rn(f) taken over all radio labelings f of G. A graph G on n vertices is radio graceful if and only if rn(G) = n. In this paper, we define the radiatic dimension of G to be the smallest
positive integer k, such that the sequence of injective functions fi: V (G) → {1, 2, 3, . . . , n}, 1 ≤ i ≤ k, satisfy the condition that for every two distinct vertices u, v ∈ V (G), |fi(u)−fi(v)| ≥ diam(G)+ 1−d(u, v) for some i and denote it by rd(G). Hence a graph is radio graceful if and only if rd(G) = 1. In this paper we study the radiatic dimension of some standard g