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Pseudo-Skolem sequences and graph Skolem labelling

David A. Pike, Asiyeh Sanaei, Nabil Shalaby


Pseudo-Skolem sequences, which are similar to Skolem-type sequences in their structure and applications, are introduced. Constructions of such sequences, either directly or via the use of known Skolem-type sequences, are presented. The applicability of these sequences to Skolem labelled graphs, in particular classes of rail-siding graphs and caterpillars, are also discussed.

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Baker, C., Kergin, P., and Bonato, A., Skolem arrays and Skolem labellings of ladder graphs, Ars Combin. 63 (2002), 97–107.

Baker, C. A. and Manzer, J. D. A., Skolem-labeling of generalized three-vane windmills, Australas. J. Combin. 41 (2008), 175–204.

Biraud, F., Blum, E. J., and Ribes, J. C., On optimum synthetic linear arrays with application to radioastronomy, IEEE Trans. Antennas and Propagation 22 (1974), no. 1, 108–109.

Dyer, D. and McKay, N., Skolem-labeling of $k$-regular caterpillars, preprint, 2006.

Graham, A. J., Pike, D. A., and Shalaby, N., Skolem labelled trees and $P_s,square ,P_t$ Cartesian products, Australas. J. Combin. 38 (2007), 101–115.

Mendelsohn, E. and Shalaby, N., Skolem labelled graphs, Discrete Math. 97 (1991), no. 1-3, 301–317.

Mendelsohn, E. and Shalaby, N., On Skolem labelling of windmills, Ars Combin. 53 (1999), 161–172.

O'Keefe, E. S., Verification of a conjecture of Th. Skolem, Math. Scand. 9 (1961), 80–82.

Shalaby, N., The existence of near-Skolem and hooked near-Skolem sequences, Discrete Math. 135 (1994), no. 1-3, 303–319.

Shalaby, N., The existence of near-Rosa and hooked near-Rosa sequences, Discrete Math. 261 (2003), no. 1-3, 435–450.

Skolem, Th., On certain distributions of integers in pairs with given differences, Math. Scand. 5 (1957), 57–68.



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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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