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Tree (graph theory)

In graph theory, a tree is an undirected graph in which every pair of distinct vertices is connected by exactly one path, or equivalently, a connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees.

Definitions, Properties & Enumeration

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Explore the main themes, entities and connections around Tree (graph theory). Start with the topic map, then use the sections below for research and deeper semantic analysis.

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Key facts & relationships

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

Chromatic number
2 if v > 1
Edges
v − 1
Vertices
v

Topics to explore

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Overview

Definitions

Properties

Enumeration

Types of trees

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.

Map overview Semantic statistics

Tree (graph theory)

Nodes72
Edges71
Triples5
Avg. degree1.97
Density0.027778
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Tree (graph theory)

Top relations

Chromatic number · 1
Tree (graph theory) → 2 if v 1
Edges · 1
Tree (graph theory) → v − 1
Vertices · 1
Tree (graph theory) → v

Important terminology Word statistics

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

Important terminology

tree vertex graph vertices trees connected rooted path edges acyclic directed forest every root undirected one number two called case

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Tree (graph theory)Chromatic number2 if v > 11.00infobox
Tree (graph theory)Edgesv − 11.00infobox
Tree (graph theory)Verticesv1.00infobox
an ordering of the neighbors at each vertexinstance ofoften with an additional structure0.80text
are a key data structure in computer scienceinstance ofoften with an additional structure0.80text

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
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