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Everything about Permutation graph
Graph representing a permutation
In the mathematical field of graph theory, a permutation graph is a graph whose vertices represent the elements of a permutation, and whose edges represent pairs of elements that are reversed by the permutation. Permutation graphs may also be defined geometrically, as the intersection graphs of line segments whose endpoints lie on two parallel lines. Different permutations may give rise to the same permutation graph; a given graph has a unique representation if it is prime with respect to the modular decomposition. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Permutation graphA 5-minute orientation
- Skim a recent paper: Multiscale permutation entropy based on natural visibility graph and its application to rolling bearing fault diagnosisInfluential work since 2022
- Pick up a classic book: The classification of countable homogeneous directed graphs and countable homogeneous n-tournamentsThe most-reprinted book on the subject
- Read the landmark paper: Generating all graph coverings by permutation voltage assignmentsCited 177 times
- Go sideways: PathwidthA closely related topic
- Go sideways: Comparability graphA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Generating all graph coverings by permutation voltage assignments
Permutation Equivariant Graph Framelets for Heterophilous Graph Learning
Permutation Invariant Graph-to-Sequence Model for Template-Free Retrosynthesis and Reaction Prediction
Permutation-partition pairs: a combinatorial generalization of graph embeddings
Permutation Entropy for Graph Signals
Metric invariance in exploratory graph analysis via permutation testing
On graph-restrictive permutation groups
Finding a minimum independent dominating set in a permutation graph
🆕 Influential since 2022
Multiscale permutation entropy based on natural visibility graph and its application to rolling bearing fault diagnosis
Graph Multi-Scale Permutation Entropy for Bearing Fault Diagnosis
Learning to Optimize Permutation Flow Shop Scheduling via Graph-Based Imitation Learning
PINE: Universal Deep Embedding for Graph Nodes via Partial Permutation Invariant Set Functions
Permutation-invariant representations with applications to graph deep learning
📚 Books worth reading
The classification of countable homogeneous directed graphs and countable homogeneous n-tournamentsGregory L. Cherlin · 1998
Group-theoretic algorithms and graph isomorphismChristoph M. Hoffmann · 1982
Davenport-Zannier Polynomials and Dessins D'EnfantsNikolai M. Adrianov, Fedor Pakovich · 2020- 📕A foundation for PROPs, algebras, and modulesDonald Y. Yau · 2015
- 📕Topics in Hyperplane ArrangementsMarcelo Aguiar, Swapneel Mahajan · 2017
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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