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Title: Word-graph theory : on the structural characterisation of word-respectable digraphs
Author: Bell, Edward J. L.
Awarding Body: Lancaster University
Current Institution: Lancaster University
Date of Award: 2012
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A word- graph Gw is a simple digraph associated with a finite word w such that the vertex set of Gw is the alphabet of wand the edge-set of Gw is determined by ~on-identical adjacent letter pairs in w. A family of word-graphs can be thought of as a formal language. The novel theory of word- graphs proposed in this thesis is of interest for two reasons: . first, word-graphs have close links with a range of word-based stochastic processes such as language, music, DNA and protein sequences; second, the cross-applicability of proof techniques in graph theory and combinatorics on words has lead to a recent explosion of interest in the literature in the relationship between words and graphs. The focus of this thesis is on developing a theory of word-graphs by formalising how structural word-theoretic properties manifest in digraphs and how structural graphtheoretic properties manifest in words. The analysis starts by looking at the relationship between word and digraph forms and continues by investigating whether or not a given digraph can be represented by a word or a set of words. The main findings include: representational word and digraph structure is intrinsically linked; every finite digraph can be represented by a finite set of words; and the number of words required to represent a digraph is determined by that digraph's edge-contracted subgraphs. Besides the theory's applications in stochastic process analysis, word- graph theory has the potential to be used as a general methodology for digraph and word theoretic analysis.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available