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Ptolemaic graph

In graph theory, a Ptolemaic graph is an undirected graph whose shortest path distances obey Ptolemy's inequality, which in turn was named after the Greek astronomer and mathematician Ptolemy. The Ptolemaic graphs are exactly the graphs that are both chordal and distance-hereditary; they include the block graphs and are a subclass of the perfect graphs.

Characters, Characterization & Enumeration

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Characterization

VerticesGem graphMaximal cliquesSeparatorCycle
10 related topics

Enumeration

Generating functionSymbolicallyOEIS
3 related topics

Overview

Graph theoryUndirected graphShortest pathPtolemy's inequalityGreek
12 related topics

Computational complexity

Linear time
1 related topics

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Overview

Characterization

Computational complexity

Enumeration

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Map overview Semantic statistics

Ptolemaic graph

Nodes31
Edges30
Triples17
Avg. degree1.94
Density0.064516
Components1

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Ptolemaic graph

Top relations

related to Characterization · 11
Ptolemaic graph → Because, Every, For, In, Ptolemaic, Ptolemy's, That, The, The Hasse, These, To
related to Enumeration · 3
Ptolemaic graph → Based, Ptolemaic, The
related to Computational complexity · 2
Ptolemaic graph → Based, Ptolemaic
is a · 1
Ptolemaic graph → undirected graph whose shortest path distances obey Ptolemy's inequality

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Important terminology

graph ptolemaic distance-hereditary vertices chordal graphs every gem shortest path induced form distances greater two cliques whole contain convex obey

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Ptolemaic graphis aundirected graph whose shortest path distances obey Ptolemy's inequality0.90text
Ptolemaic graphrelated to CharacterizationPtolemaic0.60section
Ptolemaic graphrelated to CharacterizationThe0.60section
Ptolemaic graphrelated to CharacterizationPtolemy's0.60section
Ptolemaic graphrelated to CharacterizationFor0.60section
Ptolemaic graphrelated to CharacterizationIn0.60section
Ptolemaic graphrelated to CharacterizationEvery0.60section
Ptolemaic graphrelated to CharacterizationBecause0.60section
Ptolemaic graphrelated to CharacterizationThese0.60section
Ptolemaic graphrelated to CharacterizationTo0.60section
Ptolemaic graphrelated to CharacterizationThe Hasse0.60section
Ptolemaic graphrelated to CharacterizationThat0.60section

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