Constructions of antimagic labelings for some families of regular graphs

constructions of antimagic labelings for some families of regular graphs

in this paper we construct antimagic labelings of the regular complete multipartite graphs and we also extend the construction to some families of regular graphs.

Antimagic Labelings of Weighted and Oriented Graphs∗

A graph G is k–weighted–list–antimagic if for any vertex weighting ω : V (G) → R and any list assignment L : E(G)→ 2R with |L(e)| ≥ |E(G)|+k there exists an edge labeling f such that f(e) ∈ L(e) for all e ∈ E(G), labels of edges are pairwise distinct, and the sum of the labels on edges incident to a vertex plus the weight of that vertex is distinct from the sum at every other vertex. In this pa...

On d-antimagic labelings of plane graphs

The paper deals with the problem of labeling the vertices and edges of a plane graph in such a way that the labels of the vertices and edges surrounding that face add up to a weight of that face. A labeling of a plane graph is called d-antimagic if for every positive integer s, the s-sided face weights form an arithmetic progression with a difference d. Such a labeling is called super if the sm...

Vertex-antimagic total labelings of graphs

In this paper we introduce a new type of graph labeling, the (a, d)vertex-antimagic total labeling, which is a generalization of several other types of labelings. A connected graph G(V, E) is said to be (a, d)-vertex-antimagic total if there exist positive integers a, d and a bijection λ : V ∪ E → {1, 2, . . . , |V | + |E|} such that the induced mapping gλ : V → W is also a bijection, where W =...

Regular Graphs are Antimagic

In this note we prove with a slight modification of an argument of Cranston et al. [2] that k-regular graphs are antimagic for k ≥ 2.

Some constructions of supermagic non-regular graphs