Let Γ=(V,E) be a graph of order n. A closed distance magic labeling Γ is bijection ℓ:V→{1,2,…,n} for which there exists positive integer r such that ∑x∈N[u]ℓ(x)=r all vertices u∈V, where N[u] the neighborhood u. said to if it admits labeling. In this paper, we classify connected circulants with valency at most 5, is, Cayley graphs Cay(Zn;S) |S|≤5, S=−S, 0∉S and S generates Zn.

A graph Γ=(V,E) of order n is distance magic if it admits a bijective labeling ℓ:V→{1,2,…,n} its vertices for which there exists positive integer κ such that ∑u∈N(v)ℓ(u)=κ all v∈V, where N(v) the neighborhood v. circulant admitting an automorphism cyclically permuting vertices. In this paper we study circulants valency 6. We obtain some necessary and sufficient conditions 6 to be magic, thereby...

Graph labeling is an important area of research in Graph theory. There are many kinds of graph labeling such as Graceful labeling, Magic labeling, Prime labeling, and other different labeling techniques.In this paper the Prime labeling of certain classes of graphs are discussed.It is of interest to note that H-graph which is a 3 –regular graph satisfy Prime labeling. A Gear graph is a graph obt...

A vertex magic total (VMT) labeling of a graph G = (V,E) is a bijection from the set of vertices and edges to the set of integers defined by λ : V ∪E → {1, 2, . . . , |V | + |E|} so that for every x ∈ V , w(x) = λ(x)+ ∑ xy∈E λ(xy) = k, for some integer k. A VMT labeling is said to be a super VMT labeling if the vertices are labeled with the smallest possible integers, 1, 2, . . . , |V |. In thi...

An edge-magic total labeling on G is a one-to-one map λ from V (G) ∪ E(G) onto the integers 1, 2, . . . , |V (G) ∪ E(G)| with the property that, given any edge (x, y), λ(x) + λ(x, y) + λ(y) = k for some constant k. The labeling is strong if all the smallest labels are assigned to the vertices. Enomoto et al. proved that a graph admitting a strong labeling can have at most 2|V (G)| − 3 edges. In...