Abstract
A graph G is called super edge-magic if there exists a one-to-one mapping f from V(G)υE(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 GυnK 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. © 2008 Springer Berlin Heidelberg.
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CITATION STYLE
Ngurah, A. A. G., Baskoro, E. T., Simanjuntak, R., & Uttunggadewa, S. (2008). On Super edge-magic strength and deficiency of graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4535 LNCS, pp. 144–154). Springer Verlag. https://doi.org/10.1007/978-3-540-89550-3_16
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