Starter sequences: generalizations and applications

Omer, Farej (2018) Starter sequences: generalizations and applications. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

In this thesis we introduce new types of starter sequences, pseudo-starter sequences, starter-labellings, and generalized (extended) starter sequences. We apply these new sequences to graph labeling. All the necessary conditions for the existence of starter, pseudo-starter, extended, m-fold, excess, and generalized (extended) starter sequences are determined, and some of these conditions are shown to be sufficient. The relationship between starter sequences and graph labellings is introduced. Moreover, the starter-labeling and the minimum hooked starter-labeling of paths, cycles, and k- windmills are investigated. We show that all paths, cycles, and k-windmills can be starter-labelled or minimum starter-labelled.

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