On (a,1)-Vertex-Antimagic Edge Labeling of Regular Graphs
An (a,s)-vertex-antimagic edge labeling (or an (a,s)-VAE labeling, for short) of G is a bijective mapping from the edge set E(G) of a graph G to the set of integers 1,2,…,|E(G)| with the property that the vertex-weights form an arithmetic sequence starting from a and having common difference s, wher...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/320616 |
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| author | Martin Bača Andrea Semaničová-Feňovčíková Tao-Ming Wang Guang-Hui Zhang |
| author_facet | Martin Bača Andrea Semaničová-Feňovčíková Tao-Ming Wang Guang-Hui Zhang |
| author_sort | Martin Bača |
| collection | DOAJ |
| description | An (a,s)-vertex-antimagic edge labeling (or an (a,s)-VAE labeling, for short) of G is a bijective mapping from the edge set E(G) of a graph G to the set of integers 1,2,…,|E(G)| with the property that the vertex-weights form an arithmetic sequence starting from a and having common difference s, where a and s are two positive integers, and the vertex-weight is the sum of the labels of all edges incident to the vertex. A graph is called (a,s)-antimagic if it admits an (a,s)-VAE labeling. In this paper, we investigate the existence of (a,1)-VAE labeling for disconnected 3-regular graphs. Also, we define and study a new concept (a,s)-vertex-antimagic edge deficiency, as an extension of (a,s)-VAE labeling, for measuring how close a graph is away from being an (a,s)-antimagic graph. Furthermore, the (a,1)-VAE deficiency of Hamiltonian regular graphs of even degree is completely determined. More open problems are mentioned in the concluding remarks. |
| format | Article |
| id | doaj-art-e93d41ad687340738161a3471d29f659 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e93d41ad687340738161a3471d29f6592025-02-03T01:08:06ZengWileyJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/320616320616On (a,1)-Vertex-Antimagic Edge Labeling of Regular GraphsMartin Bača0Andrea Semaničová-Feňovčíková1Tao-Ming Wang2Guang-Hui Zhang3Department of Applied Mathematics and Informatics, Technical University, Letná 9, 04200 Košice, SlovakiaDepartment of Applied Mathematics and Informatics, Technical University, Letná 9, 04200 Košice, SlovakiaDepartment of Applied Mathematics, Tunghai University, Taichung 40704, TaiwanDepartment of Applied Mathematics, National Chung Hsing University, Taichung 402, TaiwanAn (a,s)-vertex-antimagic edge labeling (or an (a,s)-VAE labeling, for short) of G is a bijective mapping from the edge set E(G) of a graph G to the set of integers 1,2,…,|E(G)| with the property that the vertex-weights form an arithmetic sequence starting from a and having common difference s, where a and s are two positive integers, and the vertex-weight is the sum of the labels of all edges incident to the vertex. A graph is called (a,s)-antimagic if it admits an (a,s)-VAE labeling. In this paper, we investigate the existence of (a,1)-VAE labeling for disconnected 3-regular graphs. Also, we define and study a new concept (a,s)-vertex-antimagic edge deficiency, as an extension of (a,s)-VAE labeling, for measuring how close a graph is away from being an (a,s)-antimagic graph. Furthermore, the (a,1)-VAE deficiency of Hamiltonian regular graphs of even degree is completely determined. More open problems are mentioned in the concluding remarks.http://dx.doi.org/10.1155/2015/320616 |
| spellingShingle | Martin Bača Andrea Semaničová-Feňovčíková Tao-Ming Wang Guang-Hui Zhang On (a,1)-Vertex-Antimagic Edge Labeling of Regular Graphs Journal of Applied Mathematics |
| title | On (a,1)-Vertex-Antimagic Edge Labeling of Regular Graphs |
| title_full | On (a,1)-Vertex-Antimagic Edge Labeling of Regular Graphs |
| title_fullStr | On (a,1)-Vertex-Antimagic Edge Labeling of Regular Graphs |
| title_full_unstemmed | On (a,1)-Vertex-Antimagic Edge Labeling of Regular Graphs |
| title_short | On (a,1)-Vertex-Antimagic Edge Labeling of Regular Graphs |
| title_sort | on a 1 vertex antimagic edge labeling of regular graphs |
| url | http://dx.doi.org/10.1155/2015/320616 |
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