A vertex-magic group edge labeling of a graph G(V,E) with |E| = n is an injection from E to an abelian group Γ of order n such that the sum of labels of all incident edges of every vertex x ∈ V is equal to the same element μ ∈ Γ. We completely characterize all Cartesian products Cn Cm that admit a vertex-magic group edge labeling by Z2nm, as well as provide labelings by a few other finite abeli...

A group distance magic labeling of a graph G(V, E) with |V | = n is an injection from V to an abelian group Γ of order n such that the sum of labels of all neighbors of every vertex x ∈ V is equal to the same element μ ∈ Γ. We completely characterize all Cartesian products Ck Cm that admit a group distance magic labeling by Zkm.

Let A be an abelian group. An A-magic of a graph G = (V, E) is a labeling f : E(G) → A\{0} such that the sum of the labels of the edges incident with u ∈ V is a constant, where 0 is the identity element of the group A. In this paper we prove Z3-magic labeling for the class of even cycles, Bistar, ladder, biregular graphs and for a certain class of Cayley digraphs. Mathematics Subject Classifica...

An anti-magic labeling of a finite simple undirected graph with p vertices and q edges is a bijection from the set of edges to the integers {1, ..., q} such that all p vertex sums are pairwise distinct, where the vertex sum on a vertex is the sum of labels of all edges incident to such vertex. A graph is called anti-magic if it has an anti-magic labeling. Hartsfield and Ringel [3] conjectured t...

In this work labeling of planar graphs is taken up which involves labeling the p vertices, the q edges and the f internal faces such that the weights of the faces form an arithmetic progression with common difference d. If d = 0, then the planar graph is said to have an Inner Magic labeling; and if d = 0, then it is Inner Antimagic labeling. Some new kinds of graphs have been developed which ha...

A simple graph G admits an H-covering if every edge in E(G) belongs to a subgraph of G isomorphic to H. The graph G is H−magic if there exists a bijection f : V (G) [ E(G) ! {1, 2, 3, · · · , |V (G) [ E(G)|} such that for every subgraph H0 P of G isomorphic to H. G is said to be H − supermagic if f(V (G)) = {1, 2, 3, · · · , |V (G)|}. In thi...