Algebraic Investigation of Connected Components

  • Roland Glück
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10226)


This paper characterizes connected components of both directed and undirected graphs as atomic fixpoints. As algebraic structure for our investigations we combine complete Boolean algebras with the well-known theory of Kleene Algebra with domain. Using diamond operators as an algebraic generalization of relational image and preimage we show how connected components can be modeled as atomic fixpoints of functions operating on tests and prove some advanced theorems concerning connected components.


Directed Acyclic Graph Undirected Graph Relation Algebra Diamond Operator Complete Boolean Algebra 
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.



The author is grateful to Bernhard Möller and the anonymous reviewers for thorough proofreading and valuable hints and remarks which helped to improve the paper.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Deutsches Zentrum für Luft- und RaumfahrtAugsburgGermany

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