Vertex-antimagic labelings of regular graphs
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Let G = (V,E) be a finite, simple and undirected graph with p vertices and q edges. An (a, d)-vertex-antimagic total labeling of G is a bijection f from V (G) ∪ E(G) onto the set of consecutive integers 1, 2, …, p + q, such that the vertex-weights form an arithmetic progression with the initial term a and difference d, where the vertex-weight of x is the sum of the value f(x) assigned to the vertex x together with all values f(xy) assigned to edges xy incident to x. Such labeling is called super if the smallest possible labels appear on the vertices.
In this paper, we study the properties of such labelings and examine their existence for 2r-regular graphs when the difference d is 0, 1, …, r + 1.
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About this Article
- Vertex-antimagic labelings of regular graphs
Acta Mathematica Sinica, English Series
Volume 28, Issue 9 , pp 1865-1874
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- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Additional Links
- Super vertex-antimagic total labeling
- vertex-antimagic edge labeling
- regular graph
- Author Affiliations