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Group based graph transformations and hierarchical representations of graphs

  • A. Ehrenfeucht
  • T. Harju
  • G. Rozenberg
Structure and Logic of Graphs
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1073)

Abstract

A labeled 2-structure, 2s for short, is a complete edge-labeled directed graph without loops or multiple edges. An important result of the theory of 2-structures is the existence of a hierarchical representation of each 2s. A δ-reversible labeled 2-structure g will be identified with its labeling function that maps each edge (x, y), x ≠ y, of the domain D into a group Δ so that g(y, x)=δ(g(x, y)) for an involution δ of Δ. For each mapping (selector) Δ:D → ‡ a δ-reversible 2-structure gσ is obtained from g by gσ(x, y)=ρ(x)g(x, y)δ(ρ(y)). A dynamic δ-reversible 2-structure G=[g] generated by g is the set {gσ¦ σ a selector}. We define the plane trees of G to capture the hierarchical representation of G as seen by individual elements of the domain. We show that all the plane trees are strongly related to each other. Indeed, they are all obtainable from one simple unrooted undirected tree — the form of G. Thus, quite surprisingly, all hierarchical representations of 2s's belonging to one dynamic 2s G can be combined into one hierarchical representation of G.

Keywords

Plane Tree Maximal Element Reverse Edge Label Function Hierarchical Representation 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • A. Ehrenfeucht
    • 1
  • T. Harju
    • 2
  • G. Rozenberg
    • 1
    • 3
  1. 1.Department of Computer ScienceUniversity of Colorado at BoulderBoulderUSA
  2. 2.Department of MathematicsUniversity of TurkuTurkuFinland
  3. 3.Department of Computer ScienceLeiden UniversityRA LeidenThe Netherlands

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