Some Sequence of Wrapped Δ-Labellings for the Complete Bipartite Graph

The design of large disk array architectures leads to interesting combinatorial problems. Minimizing the number of disk operations when writing to consecutive disks leads to the concept of “cluttered orderings” which were introduced for the complete graph by Cohen et al. (2001). Mueller et al. (2005) adapted the concept of wrapped Δ-labellings to the complete bipartite case. In this paper, we give some sequence in order to generate wrapped Δ-labellings as cluttered orderings for the complete bipartite graph. New sequence we give is different from the sequences Mueller et al. gave, though the same graphs in which these sequences are labeled.

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Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Adachi, T. and Kikuchi, D. (2015) Some Sequence of Wrapped Δ-Labellings for the Complete Bipartite Graph. Applied Mathematics, 6, 195-205. doi: 10.4236/am.2015.61019.

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