TL;DR
This paper introduces two monads for graphs, utilizing algebraic frameworks based on hyperedge and vertex replacement, and employs monad notation to formalize graph transformations.
Contribution
It presents a novel algebraic approach to graph theory by defining two monads for graphs, expanding the theoretical tools available for graph transformations.
Findings
Defines two monads for graphs based on hyperedge and vertex replacement
Formalizes graph transformations using monad notation
Provides a foundational algebraic framework for graph analysis
Abstract
An introduction to algebras for graphs, based on Courcelle's algebras of hyperedge replacement and vertex replacement. The paper uses monad notation.
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Taxonomy
Topicssemigroups and automata theory · Advanced Graph Theory Research · Advanced Algebra and Logic