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...

A total labeling of a graph with v vertices and e edges is defined as a one-to-one map taking the vertices and edges onto the integers 1, 2, · · · , v+e. Such a labeling is vertex magic if the sum of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vertex, and edge magic if the sum of an edge label and the labels of the endpoints of the edge ...

In this paper we present an algorithm and prove the existence of graph labelings such as Z 3 -magic, Cordial, total cordial, E-cordial, total E-cordial, Product cordial, total product cordial, Product E-cordial, total product E-cordial labelings for the Competition graph of the Cayley digraphs associated with the diheadral group D n . AMS SUBJECT CLASSIFICATION: 05C78.

In this paper we prove that the extended triplicate graph (ETG) of finite paths admits product E-cordial, total product E-cordial labelings. We show that ETG of finite paths of length n where n ∉ {4m-3|m∈N} admits E-Cordial, total E-cordial labelings and also we prove the existence of Z3 – magic labeling for the modified Extended Triplicate graph.

A total labelling of a graph with v vertices and e edges is a one-to-one map taking the vertices and edges onto the set {1, 2, 3, . . . , v + e}. A labelling can be used to define a weight for each vertex and edge. For a vertex the weight is the sum of the label of the vertex and the labels of the incident edges. For an edge {x, y} the weight is the sum of the label of the edge and the labels o...

A graph G = (V (G), E(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 H ′ of G isomorphic to H, ∑ v∈V (H′) f(v) + ∑ e∈E(H′) f(e) is constant. Then G is H-supermagic if f(V (G)) = {1, 2, 3, . . . , |V (G)|}. Let {Gi}i=1 be a fi...

ARTICLE INFO An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p+ q} such that for every copy H in the decomposition, ∑

We use multivariate splines to investigate linear diophantine equations and related problems in graph theory. In particular, we solve a conjecture of Stanley about symmetric magic squares. 0 Elsevier Science Inc., 1997