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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
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 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |