A 1-vertex-magic vertex labeling of a graph G(V,E) with p vertices is a bijection f from the vertex set V (G) to the integers 1, 2, . . . , p with the property that there is a constant k such that at any vertex x the sum ∑ f(x) taken over all neighbors of x is k. In this paper, we study the 1-vertex-magic vertex labelings of two families of disconnected graphs, namely a disjoint union of m copi...

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...

Let G(V,E) be a graph and λ be a bijection from the set V ∪E to the set of the first |V |+ |E| natural numbers. The weight of a vertex is the sum of its label and the labels of all adjacent edges. We say λ is a vertex magic total (VMT) labeling of G if the weight of each vertex is constant. We say λ is an (s, d) -vertex antimagic total (VAT) labeling if the vertex weights form an arithmetic pro...

Let A be a non-trivial, finitely-generated abelian group and A∗ = A\{0}. A graph is A-magic if there exists an edge labeling using elements of A∗ which induces a constant vertex labeling of the graph. In this paper, we analyze the group-magic property for complete n-partite graphs and composition graphs with deleted edges.

An (a, d)-edge-antimagic total labeling of a graph G with p vertices and q edges is a bijection f from the set of all vertices and edges to the set of positive integers {1, 2, 3, . . . , p + q} such that all the edge-weights w(uv) = f(u) + f(v) + f(uv);uv ∈ E(G), form an arithmetic progression starting from a and having common difference d. An (a, d)-edgeantimagic total labeling is called a sup...

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...

Let A be an abelian group with non-identity elements A∗. A graph is A-magic if it has an edge-labeling by elements of A∗ which induces a constant vertex labeling of the graph. In this paper we determine, for certain classes of triominoes and polyominoes, for which values of k ≥ 2 the graphs are Zk-magic.