A conjecture on strong magic labelings of 2-regular graphs

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...

Vertex-magic labelings of regular graphs II

Previously the first author has shown how to construct vertexmagic total labelings (VMTLs) for large families of regular graphs. The construction proceeds by successively adding arbitrary 2-factors to a regular graph of order n which possesses a strong VMTL, to produce a regular graph of the same order but larger size. In this paper, we exploit this construction method. We are able to show that...

Vertex magic total labelings of 2-regular graphs

A vertex magic total (VMT) labeling of a graph G = (V,E) is a bijection from the set of vertices and edges to the set of integers defined by λ : V ∪E → {1, 2, . . . , |V | + |E|} so that for every x ∈ V , w(x) = λ(x)+ ∑ xy∈E λ(xy) = k, for some integer k. A VMT labeling is said to be a super VMT labeling if the vertices are labeled with the smallest possible integers, 1, 2, . . . , |V |. In thi...

Zero-Sum Magic Labelings and Null Sets of Regular Graphs

For every h ∈ N, a graph G with the vertex set V (G) and the edge set E(G) is said to be h-magic if there exists a labeling l : E(G) → Zh\{0} such that the induced vertex labeling s : V (G) → Zh, defined by s(v) = ∑ uv∈E(G) l(uv) is a constant map. When this constant is zero, we say that G admits a zero-sum h-magic labeling. The null set of a graph G, denoted by N(G), is the set of all natural ...

Totally magic labelings of graphs