Some results on super mean graphs - Jeyanthi P.; Ramya D. (Utilitas Mathematica, 2013)
Let G(V, E) be a graph with p vertices and q edges 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]. Then f is called a super mean labeling of G if f(V(G)) ∪f(e): e ε 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 prove that <Sm, n:Pm+1>, <P2mô K1,n > and caterpillar are super mean graphs. We further establish that if T is a Tp-tree then T ⊙ Kn is also a super mean graph.