Disconnected graphs with magic labelings

Totally magic labelings of graphs

Distance magic labelings of graphs

As a natural extension of previously defined graph labelings, we introduce in this paper a new magic labeling whose evaluation is based on the neighbourhood of a vertex. We define a 1-vertex-magic vertex labeling of a graph with v vertices as a bijection f taking the vertices to the integers 1, 2, . . . , v with the property that there is a constant k such that at any vertex x, ∑ y∈N(x) f(y) = ...

Magic labelings of regular graphs

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...

Ring-magic labelings of graphs

In this paper, a generalization of a group-magic graph is introduced and studied. Let R be a commutative ring with unity 1. A graph G = (V,E) is called R-ring-magic if there exists a labeling f : E → R−{0} such that the induced vertex labelings f : V → R, defined by f(v) = Σf(u, v) where (u, v) ∈ E, and f : V → R, defined by f(v) = Πf(u, v) where (u, v) ∈ E, are constant maps. General algebraic...

Super Vertex-magic Total Labelings of Graphs

Let G be a finite simple graph with v vertices and e edges. A vertex-magic total labeling is a bijection λ from V (G)∪E(G) to the consecutive integers 1, 2, · · · , v+e with the property that for every x ∈ V (G), λ(x) + Σy∈N(x)λ(xy) = k for some constant k. Such a labeling is super if λ(V (G)) = {1, · · · , v}. We study some of the basic properties of such labelings, find some families of graph...