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Ptolemaic graph: Characters, Characterization & Enumeration

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.

Language: English [EN]
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Ptolemaic graph topic overview

The analysis highlights Characters, Characterization and Enumeration as prominent areas in the source structure around Ptolemaic graph.

Related topics
26
Source areas
4
Connected nodes
30
Extracted relationships
17
Concept neighborhoods
22
Bridge connections
30

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Overview · 12 topics
Characterization · 10 topics
Enumeration · 3 topics
Computational complexity · 1 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Characterization

Computational complexity

Enumeration

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Ptolemaic graph connects Entity context

The extracted context around Ptolemaic graph shows recurring relationship patterns in the source. For example, Ptolemaic graph → Because, Every, For, In, Ptolemaic, Ptolemy's, That, The, The Hasse, These, To Another extracted example is Ptolemaic graph → Based, Ptolemaic, The. Use these groups to spot repeated connection types before inspecting the individual relationships.

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

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

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

Ptolemaic graph relationships Subject–Predicate–Object triples

TTTA extracted 17 structured relationships around Ptolemaic graph. Examples in this analysis include Ptolemaic graph → is a → undirected graph whose shortest path distances obey Ptolemy's inequality and Ptolemaic graph → related to Characterization → Ptolemaic. The table shows each extracted connection, where it came from and its confidence.

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

Related concept clusters Concept neighborhoods

The concept neighborhoods around Ptolemaic graph bring nearby vocabulary together. In this analysis, examples include Graphs, Induced and Distances. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Ptolemaic graph
    • Graphs
    • Induced
    • Distances
    • Vertices
    • Characterization
    • Inequality
    • Obey
    • Perfect
    • Ptolemy's
    • Exception
    • Operations
    • Subgraph
  • ptolemaic graph
    • Graphs
    • Induced
    • Gem
    • Distance-hereditary
    • Distances
    • Greater
    • Chordal
    • Vertices
    • Characterization
    • Inequality
    • Obey
    • Perfect
  • graph theory
    • Induced
    • Gem
    • Distance-hereditary
    • Distances
    • Greater
    • Chordal
    • Exception
    • Illustration
    • Inequality
    • Obey
    • Operations
    • Ptolemy's
  • undirected graph
    • Induced
    • Gem
    • Distance-hereditary
    • Distances
    • Greater
    • Chordal
    • Exception
    • Illustration
    • Inequality
    • Obey
    • Operations
    • Ptolemy's
  • gem graph
    • Illustration
    • Induced
    • Gem
    • Graph
    • Distance-hereditary
    • Greater
    • Distances
    • Chordal
    • Exception
    • Inequality
    • Obey
    • Operations
  • chordal
    • Distance-hereditary
    • Induced
    • Perfect
    • Subgraph
    • Greater
    • Whole
    • Gem
    • Graph
    • Graphs
    • Cycle
    • Diagonals
    • Ptolemaic
  • distance-hereditary
    • Induced
    • Graph
    • Perfect
    • Subgraph
    • Three
    • Greater
    • Whole
    • Graphs
    • Ptolemaic
    • Cycle
    • Exception
    • Operations
  • shortest path
    • Shortest
    • Inequality
    • Obey
    • Ptolemy's
    • Every
    • Vertices
    • Convex
    • Greek
    • Mathematician
    • Ptolemy
    • Characterization
    • Vertex

Connections between topic areas Semantic bridges

For Ptolemaic graph, one of the stronger structural bridges in this analysis connects Ptolemaic graph with Overview. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Ptolemaic graph — Overview · splits 18 ⟂ 13
Ptolemaic graph — Characterization · splits 20 ⟂ 11
Ptolemaic graph — Enumeration · splits 27 ⟂ 4

Map overview Semantic statistics

Ptolemaic graph

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

Source & methodology

TTTA analyzes the structure around Ptolemaic graph to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Characters, Characterization & Enumeration, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Ptolemaic graph · EN edition · Analysis: TopicsToTalkAbout

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