Here our discussion is on a three star graph which is finite, simple and undirected one. For notations and terminology, we follow [1]. The vertex set and the edge set of a graph G are denoted by V (G) and E (G) respectively. So G(V,E) is a graph with p vertices and q edges. Much work is done by researchers on Mean labeling and Super mean labeling of graphs applying them on a variety of graphs [2-7,9,10]. Motivated by these work the concept of SSML(V4,E2) on a two star graph was introduced by Uma Maheshwari et al [8]. After a discussion on SSML(V4,E2) on a two star graphs, we were inspired to apply SSML(V4,E2) on three star graphs and hence this paper. Here the word sub is used thereby allowing omissions which lead to repetitions and a special case SSML(V4,E2). A study on omissions and repetitions on a three star graphs is done which admits SSML(V4,E2) and the formula is obtained in terms of, mand n in this paper.

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Let G be a (p, q) graph and f : V (G) → {1, 2, 3, , p + q} be an injection. For each edge e = uv, let f * (e) = f (u) + f (v) 2 if f (u) + f (v) is even and f * (e) = f (u) + f (v) + 1 2 if f (u) + f (v) is odd. Then f is called super mean labeling if f(V) ∪ {f * (e) : e ∈ E(G)} = {1, 2, 3, , p + q}. A graph that admits a super mean labeling is called a super mean graph. In this paper we with an edge in common is a super mean graph if and only if |m − n| ≤ 1.