Abstract
This paper deals with the labeling of vertices and edges of a graph. Let G be a graph with vertex set V and edge set E, where |V| be the number of vertices and |E| edges of G. The two bijection methods for which we have designed algorithms are as follows. Initially A bijection λ 1:V∪E → {1, 2…|V| + |E|} is called a Vertex-Magic Total Labeling (VMTL) if there is a vertex magic constant vk such that the weight of vertex m is, λ 1(m) + Σ n εA (m) λ 1(mn) = vk, ∀ m εv Where A(m) is the set of vertices adjacent to x. In the similar fashion the bijection λ 2:V∪E → {1, 2…|V| + |E|} is called Edge-Magic Total Labeling (EMTL) if there is a edge magic constant ek such that the weight of an edge es(mn), λ 2(m) + λ 2(n) + λ 2 e(mn) = ek, ∀ e εE. A resultant Graph which consists of both VMTL and EMTL are said to be Total Magic Labeling (TML) for different vertex magic constant and edge magic constant values. Baker and Sawada proposed algorithms to find VMTLs on cycles and wheels. In this paper we enhanced these algorithms and also we proposed new algorithms to generate EMTLs and TMLs of cycles and wheels. We used the concept variations and sum set sequences to produce VMTLs and EMTLs on cycles and wheels. Also we designed modules to identify TML’s.
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References
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© 2014 Springer International Publishing Switzerland
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Prasanna, N.L., Sudhakar, N. (2014). Enhanced Algorithms for VMTL, EMTL and TML on Cycles and Wheels. In: Satapathy, S., Avadhani, P., Udgata, S., Lakshminarayana, S. (eds) ICT and Critical Infrastructure: Proceedings of the 48th Annual Convention of Computer Society of India- Vol II. Advances in Intelligent Systems and Computing, vol 249. Springer, Cham. https://doi.org/10.1007/978-3-319-03095-1_19
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DOI: https://doi.org/10.1007/978-3-319-03095-1_19
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03094-4
Online ISBN: 978-3-319-03095-1
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