New Results on the (Super) Edge-Magic Deficiency of Chain Graphs
Let G be a graph of order v and size e. An edge-magic labeling of G is a bijection f:V(G)∪E(G)→{1,2,3,…,v+e} such that f(x)+f(xy)+f(y) is a constant for every edge xy∈E(G). An edge-magic labeling f of G with f(V(G))={1,2,3,…,v} is called a super edge-magic labeling. Furthermore, the edge-magic defic...
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| Format: | Article |
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Wiley
2017-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2017/5156974 |
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| author | Ngurah Anak Agung Gede Adiwijaya |
| author_facet | Ngurah Anak Agung Gede Adiwijaya |
| author_sort | Ngurah Anak Agung Gede |
| collection | DOAJ |
| description | Let G be a graph of order v and size e. An edge-magic labeling of G is a bijection f:V(G)∪E(G)→{1,2,3,…,v+e} such that f(x)+f(xy)+f(y) is a constant for every edge xy∈E(G). An edge-magic labeling f of G with f(V(G))={1,2,3,…,v} is called a super edge-magic labeling. Furthermore, the edge-magic deficiency of a graph G, μ(G), is defined as the smallest nonnegative integer n such that G∪nK1 has an edge-magic labeling. Similarly, the super edge-magic deficiency of a graph G, μs(G), is either the smallest nonnegative integer n such that G∪nK1 has a super edge-magic labeling or +∞ if there exists no such integer n. In this paper, we investigate the (super) edge-magic deficiency of chain graphs. Referring to these, we propose some open problems. |
| format | Article |
| id | doaj-art-4a04c5da051f4283ab7ccff52f461ff2 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-4a04c5da051f4283ab7ccff52f461ff22025-02-03T06:01:22ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252017-01-01201710.1155/2017/51569745156974New Results on the (Super) Edge-Magic Deficiency of Chain GraphsNgurah Anak Agung Gede0Adiwijaya1Department of Civil Engineering, Universitas Merdeka Malang, Jl. Taman Agung No. 1, Malang 65146, IndonesiaSchool of Computing, Telkom University, Jl. Telekomunikasi No. 1, Bandung 40257, IndonesiaLet G be a graph of order v and size e. An edge-magic labeling of G is a bijection f:V(G)∪E(G)→{1,2,3,…,v+e} such that f(x)+f(xy)+f(y) is a constant for every edge xy∈E(G). An edge-magic labeling f of G with f(V(G))={1,2,3,…,v} is called a super edge-magic labeling. Furthermore, the edge-magic deficiency of a graph G, μ(G), is defined as the smallest nonnegative integer n such that G∪nK1 has an edge-magic labeling. Similarly, the super edge-magic deficiency of a graph G, μs(G), is either the smallest nonnegative integer n such that G∪nK1 has a super edge-magic labeling or +∞ if there exists no such integer n. In this paper, we investigate the (super) edge-magic deficiency of chain graphs. Referring to these, we propose some open problems.http://dx.doi.org/10.1155/2017/5156974 |
| spellingShingle | Ngurah Anak Agung Gede Adiwijaya New Results on the (Super) Edge-Magic Deficiency of Chain Graphs International Journal of Mathematics and Mathematical Sciences |
| title | New Results on the (Super) Edge-Magic Deficiency of Chain Graphs |
| title_full | New Results on the (Super) Edge-Magic Deficiency of Chain Graphs |
| title_fullStr | New Results on the (Super) Edge-Magic Deficiency of Chain Graphs |
| title_full_unstemmed | New Results on the (Super) Edge-Magic Deficiency of Chain Graphs |
| title_short | New Results on the (Super) Edge-Magic Deficiency of Chain Graphs |
| title_sort | new results on the super edge magic deficiency of chain graphs |
| url | http://dx.doi.org/10.1155/2017/5156974 |
| work_keys_str_mv | AT ngurahanakagunggede newresultsonthesuperedgemagicdeficiencyofchaingraphs AT adiwijaya newresultsonthesuperedgemagicdeficiencyofchaingraphs |