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On linearizing graphs

  • Kurt-Ulrich Witt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 100)

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.

Keywords

Data Graph Closure Property Label Graph Linearize Scheme Finite Alphabet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Culik II, K./Maurer, H.A. "String Representations of Graphs" Rep. 50, Inst. f. Angew. Informatik u. formale Beschreibungsverfahren, Uni Karlsruhe, 1975Google Scholar
  2. [2]
    Culik II, K./Maurer, H.A. "Linearizing Selector-Graphs and Applications thereof" Angew. Informatik 9, 1977, p. 386–394Google Scholar
  3. [3]
    Inagaki, Y. et al. "Addressable Approximations to Nonaddressable Data Graphs" JCSS 17, 1978, p. 1–34Google Scholar
  4. [4]
    Majster, M.E. "Erweiterte gerichtete Graphen ein Modell für Datenstrukturen und Datenstrukturklassen" Diss. TU München, 1975Google Scholar
  5. [5]
    Rosenberg, A.L. "Data Graphs and Addressing Schemes" JCSS 5, 1971, p. 193–238Google Scholar
  6. [6]
    Rosenberg, A.L. "Generalized Addressing Schemes for Data Graphs" Math. Systems Theory 8, 1975, p. 353–366Google Scholar
  7. [7]
    Witt, K.-U. "Theorie adressiebarer Strukturen und ihrer Realisierungen" Diplom-Arbeit RWTH Aachen, 1978Google Scholar
  8. [8]
    Witt, K.-U. "Two Concepts for Linearizing Labelled Graphs" Discussion Paper 8006, Lehrst. f. Informatik III RWTH Aachen, 1980Google Scholar
  9. [9]
    Witt, K.-U. "Embedding Graphs in Discrete Spaces" Discussion Paper 8007, Lehrst. f. Informatik III RWTH Aachen, 1980Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Kurt-Ulrich Witt
    • 1
  1. 1.Lehrstuhl f. Informatik III, RWTH AachenAachen

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