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On linearizing graphs

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Graphtheoretic Concepts in Computer Science (WG 1980)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 100))

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Abstract

The notion of addressing scheme Rosenberg [5] established in his theory of data graphs and addressing schemes is used as a linearizing concept for labelled graphs. The equivalence of this concept to the graph-specification model Culik II and Maurer [2] developed to describe so called selector-graphs in a linear way is shown. Further, two constructions which modify weakly non-linearizable graphs such that their modification are linearizable are given. Some considerations on the classification of the linearizations of labelled graphs in the sense of formal language theory are made and it is proved that the class of R-regular graphs possesses regular linearizations. Finally some results concerning operations on graphs which preserve linearizability and how linearizations of graphs can be represented by two parts such that one of them is finite are given.

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References

  1. Culik II, K./Maurer, H.A. "String Representations of Graphs" Rep. 50, Inst. f. Angew. Informatik u. formale Beschreibungsverfahren, Uni Karlsruhe, 1975

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  2. Culik II, K./Maurer, H.A. "Linearizing Selector-Graphs and Applications thereof" Angew. Informatik 9, 1977, p. 386–394

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  3. Inagaki, Y. et al. "Addressable Approximations to Nonaddressable Data Graphs" JCSS 17, 1978, p. 1–34

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  4. Majster, M.E. "Erweiterte gerichtete Graphen ein Modell für Datenstrukturen und Datenstrukturklassen" Diss. TU München, 1975

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  5. Rosenberg, A.L. "Data Graphs and Addressing Schemes" JCSS 5, 1971, p. 193–238

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  6. Rosenberg, A.L. "Generalized Addressing Schemes for Data Graphs" Math. Systems Theory 8, 1975, p. 353–366

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  7. Witt, K.-U. "Theorie adressiebarer Strukturen und ihrer Realisierungen" Diplom-Arbeit RWTH Aachen, 1978

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  8. Witt, K.-U. "Two Concepts for Linearizing Labelled Graphs" Discussion Paper 8006, Lehrst. f. Informatik III RWTH Aachen, 1980

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  9. Witt, K.-U. "Embedding Graphs in Discrete Spaces" Discussion Paper 8007, Lehrst. f. Informatik III RWTH Aachen, 1980

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Authors and Affiliations

  1. Lehrstuhl f. Informatik III, RWTH Aachen, Büchel 29-31, D-5100, Aachen

    Kurt-Ulrich Witt

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  1. Kurt-Ulrich Witt
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Hartmut Noltemeier

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© 1981 Springer-Verlag Berlin Heidelberg

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Witt, KU. (1981). On linearizing graphs. In: Noltemeier, H. (eds) Graphtheoretic Concepts in Computer Science. WG 1980. Lecture Notes in Computer Science, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10291-4_3

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  • DOI: https://doi.org/10.1007/3-540-10291-4_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10291-5

  • Online ISBN: 978-3-540-38435-9

  • eBook Packages: Springer Book Archive

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