Abstract
A graph G is called super edge-magic if there exists a one-to-one mapping f from V(G) ∪ E(G) onto {1, 2, 3, ⋯ , |V(G)| + |E(G)|} such that for each uv ∈ E(G), f(u) + f(uv) + f(v) = c(f) is constant and all vertices of G receive all smallest labels. Such a mapping is called super edge-magic labeling of G. The super edge-magic strength of a graph G is defined as the minimum of all c(f) where the minimum runs over all super edge-magic labelings of G. Since not all graphs are super edge-magic, we define, the super edge-magic deficiency of a graph G as either minimum n such that G ∪ nK 1 is a super edge-magic graph or + ∞ if there is no such n. In this paper, the bound of super edge-magic strength and the super edge-magic deficiency of some families of graphs are obtained.
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Ngurah, A.A.G., Baskoro, E.T., Simanjuntak, R., Uttunggadewa, S. (2008). On Super Edge-Magic Strength and Deficiency of Graphs. In: Ito, H., Kano, M., Katoh, N., Uno, Y. (eds) Computational Geometry and Graph Theory. KyotoCGGT 2007. Lecture Notes in Computer Science, vol 4535. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89550-3_16
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DOI: https://doi.org/10.1007/978-3-540-89550-3_16
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