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Degree diameter problem: Bounds and constructions, Asymptotic behaviour & Relation to the degree–girth problem

In graph theory, the degree–diameter problem asks for the maximum possible number n d , k {\displaystyle n_{d,k}} of vertices in a finite simple undirected graph of maximum degree at most d {\displaystyle d} and diameter at most k {\displaystyle k} . A breadth-first search gives a general upper bound known as the Moore bound.

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Degree diameter problem topic overview

The analysis highlights Bounds and constructions, Asymptotic behaviour and Relation to the degree–girth problem as prominent areas in the source structure around Degree diameter problem.

Related topics
12
Source areas
5
Connected nodes
17
Related term clusters
15
Bridge connections
17

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 · 8 topics
Asymptotic behaviour · 1 topics
Bounds and constructions · 1 topics
Known values and open problems · 1 topics
Relation to the degree–girth problem · 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.

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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

Bounds and constructions

Asymptotic behaviour

Relation to the degree–girth problem

Known values and open problems

For the semantics nerds

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Advanced semantic analysis

How Degree diameter problem connects Entity context

See recurring relationship patterns around Degree diameter problem before inspecting the individual extracted relationships.

Important terminology

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

Important terminology

displaystyle diameter degree moore graph bound graphs fixed known problem every maximum vertices cycles attaining exact two possible finite upper

Degree diameter problem relationships Subject–Predicate–Object triples

TTTA extracted structured relationships around Degree diameter problem. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc

Related concept clusters Related term clusters

The concept neighborhoods around Degree diameter problem bring nearby vocabulary together. In this analysis, examples include Diameter, Problem and Graph. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Degree diameter problem
    • Diameter
    • Problem
    • Graph
    • Two
    • Maximum
    • Graphs
    • Fixed
    • Known
    • Displaystyle
    • Hoffman
    • Singleton
    • Moore
  • degree diameter problem
    • Diameter
    • Problem
    • Graph
    • Graphs
    • Two
    • Maximum
    • Fixed
    • Girth
    • Displaystyle
    • Moore
    • Known
    • Hoffman
  • graph theory
    • Attaining
    • Maximum
    • Problem
    • Bound
    • Displaystyle
    • Possible
    • Moore
    • Graphs
    • Equality
    • Hoffman
    • Singleton
    • Finite
  • maximum degree
    • Diameter
    • Problem
    • Graph
    • Two
    • Maximum
    • Largest
    • Graphs
    • Vertices
    • Fixed
    • Known
    • Displaystyle
    • Hoffman
  • diameter
    • Graph
    • Graphs
    • Two
    • Maximum
    • Problem
    • Fixed
    • Displaystyle
    • Moore
    • Known
    • Bounds
    • Largest
    • Cycles
  • moore bound
    • Moore
    • Attaining
    • Gives
    • Graphs
    • Girth
    • Graph
    • Displaystyle
    • Defect
    • Cycles
    • Equality
    • Fixed
    • Upper
  • petersen graph
    • Attaining
    • Maximum
    • Problem
    • Bound
    • Displaystyle
    • Possible
    • Moore
    • Graphs
    • Equality
    • Hoffman
    • Singleton
    • Finite
  • hoffman–singleton graph
    • Singleton
    • Attaining
    • Maximum
    • Problem
    • Bound
    • Nontrivial
    • Displaystyle
    • Possible
    • Moore
    • Odd
    • Parameter
    • Graphs

Connections between topic areas Semantic bridges

For Degree diameter problem, one of the stronger structural bridges in this analysis connects Degree diameter problem 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
Degree diameter problem — Overview · splits 9 ⟂ 9

Map overview Semantic statistics

Degree diameter problem

Nodes18
Edges17
Triples0
Avg. degree1.89
Density0.111111
Components1

Source & methodology

TTTA analyzes the structure around Degree diameter problem to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Bounds and constructions, Asymptotic behaviour & Relation to the degree–girth problem, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Degree diameter problem · EN edition · Analysis: TopicsToTalkAbout

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