A functional reformulation of UnCAL graph-transformations: or, graph transformation as graph reduction

Line graphs have been studied for over seventy years. In 1932, H. Whitney showed that for connected graphs, edge-isomorphism implies isomorphism except forK3andK1,3. The line graph transformation is one of the most widely studied of all graph transformations. In its long history, the concept has been rediscovered several times, with different names such as derived graph, interchange graph, and edge-to-vertex dual. Line graphs can also be considered as intersection graphs. Several variations and generalizations of line graphs have been proposed and studied. These include the concepts of total graphs, path graphs, and others. In this brief survey we describe these and some more recent generalizations and extensions including super line graphs and triangle graphs.

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Formalizing Architectural Refactorings as Graph Transformation Systems

Sixth International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing and First ACIS International Workshop on Self-Assembling Wireless Networks (SNPD/SAWN'05) ◽

10.1109/snpd-sawn.2005.37 ◽

2005 ◽

Cited By ~ 14

Author(s):

L. Grunske

Keyword(s):

Graph Transformation ◽

As Graph ◽

Transformation Systems ◽

Graph Transformation Systems

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Specifying Coherent Refactoring Software Artefacts with Distributed Graph Transformations

Transformation of Knowledge, Information and Data ◽

10.4018/978-1-59140-527-6.ch005 ◽

2011 ◽

pp. 95-126 ◽

Cited By ~ 6

Author(s):

Paolo Bottoni ◽

Francesco Parisi-Presicce ◽

Gabriele Taentzer

Keyword(s):

Internal Structure ◽

Graph Transformation ◽

Software System ◽

Input Output ◽

Formal Approach ◽

Computing Process ◽

Graph Transformations ◽

State Changes ◽

Uml Diagrams ◽

Refactoring Tools

This chapter discusses the use of Graph Transformations for refactoring. Refactoring changes the internal structure of a software system, while preserving its behavior. Even though the input/output view of a system’s behavior does not change, refactoring can have several consequences for the computing process, as expressed for instance by the sequence of method calls or by state changes of an object or an activity. Such modifications must be reflected in the system model, generally expressed through UML diagrams. We propose a formal approach, based on distributed graph transformation, to the coordinated evolution of code and model, as effect of refactorings. The approach can be integrated into existing refactoring tools. Due to its formal background, it makes it possible to reason about the behavior preservation of each specified refactoring.

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Introduction

Mathematical Structures in Computer Science ◽

10.1017/s0960129501003504 ◽

2002 ◽

Vol 12 (2) ◽

pp. 111-111

Author(s):

Andrea Corradini ◽

Hartmut Ehrig ◽

Grzegorz Rozenberg ◽

Gabriele Taentzer

Keyword(s):

Computer Science ◽

Graph Transformation ◽

Theoretical Point ◽

Special Issue ◽

Mathematical Structures ◽

Message Sequence Charts ◽

Graph Transformations ◽

Attributed Graphs ◽

Transformation Systems ◽

Graph Transformation Systems

This special issue of Mathematical Structures in Computer Science is devoted to the theory and applications of graph transformations. This research area dates back to the early seventies and is based on mathematical techniques from graph theory, algebra, logic and category theory. The theory of graph transformations has become attractive as a modelling and programming paradigm for complex graphical structures in a large variety of areas in computer science and for applications to other fields. During the Joint APPLIGRAPH/GETGRATS Workshop on Graph Transformation Systems (GRATRA 2000) – a satellite of ETAPS 2000 in Berlin – 35 lectures were presented by participants from all over the world. The authors of presentations that stressed the theoretical point of view were invited to submit a full version of their presentation to Mathematical Structures in Computer Science. After a careful refereeing process nine papers have been accepted, seven of which are included in this special issue.The paper by Ehrenfeucht, Petre, Prescott and Rozenberg connects the important new area of DNA computing in vivo to our area of graph transformation. An application of hypergraph constructions to the static analysis of concurrent systems is presented by König, and normal forms for context-free node rewriting hypergraph grammars by Klempien-Hinrichs. The construction of pushout complements for ‘partly total algebras’ generalising attributed graphs is presented by Burmeister, Llabrés and Roselló. Finally, Courcelle and Makowsky present operations on relational structures (generalising different kinds of graphs and hypergraphs) that are compatible with monadic second order logic. Four other accepted papers could not be included in this special issue because of space limitations.They will appear in regular issues of MSCS:— R. Heckel, M. Llabrés, H. Ehrig and F. Orejas: Concurrency and loose semantics of open graph transformation systems.— L. Helouet, C. Jard and B. Caillaud: An event structure based semantics for high-level message sequence charts.— J. Larossa and G. Valiente: Constraint satisfaction algorithms for graph pattern matching.— N. Verlinden and D. Janssens: Algebraic properties for Local Action Systems.We are most grateful to all the referees of these papers, to Olga Runge and Claudia Ermel for technical support, and to Giuseppe Longo and Cambridge University Press for fruitful cooperation in editing this special issue.

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