Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Dürer graph: Graph-theoretic properties, Dürer's solid & Symmetries

In the mathematical field of graph theory, the Dürer graph is an undirected graph with 12 vertices and 18 edges. It is named after Albrecht Dürer, whose 1514 engraving Melencolia I includes a depiction of Dürer's solid, a convex polyhedron having the Dürer graph as its skeleton. Dürer's solid is one of only four well-covered simple convex polyhedra.

Language: English [EN]
Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.
100%
More settings
100% 100% 100% 100% 100%

Dürer graph topic overview

The analysis highlights Graph-theoretic properties, Dürer's solid and Symmetries as prominent areas in the source structure around Dürer graph.

Related topics
38
Source areas
4
Connected nodes
42
Extracted relationships
29
Concept neighborhoods
26
Bridge connections
42

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.

Graph-theoretic properties · 18 topics
Overview · 11 topics
Dürer's solid · 5 topics
Symmetries · 4 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.

Key facts & relationships

High-confidence facts extracted from structured source data. Use them as anchors for further research.

Automorphisms
12 (D6)
Chromatic index
3
Chromatic number
3
Diameter
4
Edges
18
Girth
3

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

Dürer's solid

Graph-theoretic properties

Symmetries

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 Dürer graph connects Entity context

The extracted context around Dürer graph shows recurring relationship patterns in the source. For example, Dürer graph → As, Dürer, Dürer's, It, Petersen, The, The Dürer, Y-Δ Another extracted example is Dürer graph → 3-vertex-connected simple planar graph.The Dürer graph is a well-covered graph, graph formed by the vertices and edges of the Dürer solid, undirected graph with 12 vertices and 18 edges, unit distance graph. Use these groups to spot repeated connection types before inspecting the individual relationships.

Dürer graph

Top relations

related to Graph-theoretic properties · 8
Dürer graph → As, Dürer, Dürer's, It, Petersen, The, The Dürer, Y-Δ
is a · 4
Dürer graph → 3-vertex-connected simple planar graph.The Dürer graph is a well-covered graph, graph formed by the vertices and edges of the Dürer solid, undirected graph with 12 vertices and 18 edges, unit distance graph
related to Gallery · 4
Dürer graph → Dürer, Hamiltonian, The, The Dürer
related to Symmetries · 3
Dürer graph → D6, Dürer, The
Automorphisms · 1
Dürer graph → 12 (D6)
Chromatic index · 1
Dürer graph → 3
Chromatic number · 1
Dürer graph → 3
Diameter · 1
Dürer graph → 4
Edges · 1
Dürer graph → 18
Girth · 1
Dürer graph → 3

Important terminology

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

Important terminology

graph dürer solid well-covered dürer's vertices graphs convex hamiltonian mr simple cubic planar 12 edges journal polyhedron four cube doi

Dürer graph relationships Subject–Predicate–Object triples

TTTA extracted 29 structured relationships around Dürer graph. Examples in this analysis include Dürer graph → Automorphisms → 12 (D6) and Dürer graph → Chromatic index → 3. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Dürer graphAutomorphisms12 (D6)1.00infobox
Dürer graphChromatic index31.00infobox
Dürer graphChromatic number31.00infobox
Dürer graphDiameter41.00infobox
Dürer graphEdges181.00infobox
Dürer graphGirth31.00infobox
Dürer graphNamed afterAlbrecht Dürer1.00infobox
Dürer graphPropertiesCubic Planar Unit distance Well-covered1.00infobox
Dürer graphRadius31.00infobox
Dürer graphVertices121.00infobox
Dürer graphis aundirected graph with 12 vertices and 18 edges0.90text
Dürer graphis agraph formed by the vertices and edges of the Dürer solid0.90text
Dürer graphis a3-vertex-connected simple planar graph.The Dürer graph is a well-covered graph0.90text
Dürer graphis aunit distance graph0.90text

Related concept clusters Concept neighborhoods

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

  • Dürer graph
    • Dürer
    • Graph
    • Solid
    • Vertices
    • Chromatic
    • Edges
    • Number
    • Planar
    • Albrecht
    • D6
    • Depiction
    • Index
  • dürer graph
    • Dürer
    • Graph
    • Solid
    • Vertices
    • Planar
    • Chromatic
    • Edges
    • Number
    • Cube
    • Hamiltonian
    • Dürer's
    • Albrecht
  • graph theory
    • Dürer
    • Vertices
    • Doi
    • Generalized
    • Journal
    • Mr
    • Petersen
    • Solid
    • Planar
    • Graphs
    • Hamiltonian
    • Chromatic
  • undirected graph
    • Dürer
    • Vertices
    • Solid
    • Planar
    • Chromatic
    • Cube
    • Edges
    • Number
    • Hamiltonian
    • Dürer's
    • Albrecht
    • D6
  • albrecht dürer
    • Depiction
    • Named
    • Graph
    • Properties
    • Dürer's
    • D6
    • Diameter
    • Engraving
    • Girth
    • Index
    • Melencolia
    • Skeleton
  • dürer's solid
    • Solid
    • Cube
    • Engraving
    • Melencolia
    • Named
    • Skeleton
    • Vertices
    • Convex
    • D6
    • Truncated
    • Properties
    • Well-covered
  • well-covered
    • Four
    • Cubic
    • Graphs
    • One
    • Polyhedra
    • Mr
    • Number
    • Simple
    • Convex
    • Dürer's
    • Vertices
    • Solid
  • cubic graph
    • Dürer
    • Graphs
    • Diameter
    • Girth
    • Well-covered
    • Vertices
    • Properties
    • Solid
    • Planar
    • D6
    • Depiction
    • Index

Connections between topic areas Semantic bridges

For Dürer graph, one of the stronger structural bridges in this analysis connects Dürer graph with Graph-theoretic properties. 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
Dürer graphGraph-theoretic properties · splits 24 ⟂ 19
Dürer graphOverview · splits 31 ⟂ 12
Dürer graphDürer's solid · splits 37 ⟂ 6
Dürer graphSymmetries · splits 38 ⟂ 5

Map overview Semantic statistics

Dürer graph

Nodes43
Edges42
Triples29
Avg. degree1.95
Density0.046512
Components1

Source & methodology

TTTA analyzes the structure around Dürer graph to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Graph-theoretic properties, Dürer's solid & Symmetries, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

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

For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.