Vertex-antimagic labelings of regular graphs |
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| Authors: | Ali AHMAD Kashif ALI Martin BACA Petr KOVAR Andrea SEMANIC OVA-FENOVCIKOVA |
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| Affiliation: | [1]College of Computer Science and Information Systems, Jazan University, Jazan 45 142, Saudi Arabia [2]Faculty of Mathematics, COMSATS Institute of Information Technology, Lahore Campus 54000, Pakistan [3]Department of Applied Mathematics and Inforraatics, Technical University, Letnd 9, 04200 Kogice, Slovakia [4]Department of Applied Mathematics, VSB-Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic [5]Department of Applied Mathematics and Informatics, Technical University, Letnd 9, 04200 Ko~iee, Slovakia |
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| Abstract: | 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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| Keywords: | Super vertex-antimagic total labeling vertex-antimagic edge labeling regular graph |
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