On graphs with α- and <em>b</em>-edge consecutive edge magic labelings

Edge-magic total labelings

Various graph labelings that generalize the idea of a magic square have been discussed. In particular a magic labeling on a graph with v vertices and e edges will be defined as a one-to-one map taking the vertices and edges onto the integers 1, 2, ... , v+e with the property that the sum of the label on an edge and the labels of its endpoints is constant independent of the choice of edge. Prope...

On edge-magic labelings of certain disjoint unions of graphs

On consecutive edge magic total labeling of graphs

Let G = (V,E) be a finite (non-empty) graph, where V and E are the sets of vertices and edges of G. An edge magic total labeling is a bijection α from V ∪E to the integers 1,2, . . . , n+e, with the property that for every xy ∈E, α(x)+α(y)+α(xy)= k, for some constant k. Such a labeling is called an a-vertex consecutive edge magic total labeling if α(V )= {a + 1, . . . , a + n} and a b-edge cons...

On Edge-Graceful and Edge-Magic Maximal Outerplanar Graphs

Let G be a (p,q)-graph in which the edges are labeled 1,2,3,...q. The vertex sum for a vertex v is the sum of the labels of the incident edges at v. If G can be labeled so that the vertex sums are distinct, mod p, then G is said to be edgegraceful. If the edges of G can be labeled 1,2,3,...q so that the vertex sums are constant, mod p, then G is said to be edgemagic. It is conjectured by Lee [9...

Group-magic labelings and null sets of complete n-partite graphs with a deleted edge

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.