### Super Mean Labeling of Some Classes of Graphs

P Jeyanthi, D Ramya
2012 International J.Math. Combin   unpublished
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 a 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 prove that S(Pn⊙K1), S(P2×P4), S(Bn,n), Bn,n : Pm , Cn⊙K2, n ≥ 3, generalized antiprism A m n and the
more » ... double triangular snake D(Tn) are super mean graphs. Key Words: Smarandachely super m-mean labeling, Smarandachely super m-mean graph, super mean labeling, super mean graph. AMS(2010): 05C78 §1. Introduction By a graph we mean a finite, simple and undirected one. The vertex set and the edge set of a graph G are denoted by V (G) and E(G) respectively. The disjoint union of two graphs G 1 and G 2 is the graph G 1 ∪ G 2 with V (G 1 ∪ G 2) = V (G 1) ∪ V (G 2) and E(G 1 ∪ G 2) = E(G 1) ∪ E(G 2). The disjoint union of m copies of the graph G is denoted by mG. The corona G 1 ⊙ G 2 of the graphs G 1 and G 2 is obtained by taking one copy of G 1 (with p vertices) and p copies of G 2 and then joining the i th vertex of G 1 to every vertex in the i th copy of G 2. Armed crown C n ΘP m is a graph obtained from a cycle C n by identifying the pendent vertex of a path P m at each vertex of the cycle. Bi-armed crown is a graph obtained from a cycle C n by identifying the pendant vertices of two vertex disjoint paths of equal length m − 1 at each vertex of the cycle. We denote a bi-armed crown by C n Θ2P m , where P m is a path of length m − 1. The double triangular snake D(T n) is the graph obtained from the path v 1 , v 2 , v 3 ,. .. , v n by joining v i and v i+1 with two new vertices i i and w i for 1 ≤ i ≤ n− 1. The bistar B m,n is a graph obtained from 1