complete graph

完全图

Combinatorics · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

A complete graph K_n, for n ≥ 0, is a simple graph on n vertices with an edge between every pair of distinct vertices.

对 n≥0，完全图 K_n 是任意两个不同顶点都相邻的 n 阶简单图。

Example

K4K_4 has (42)=6\binom42=6 edges.

Usage and distinctions

Complete is stronger than connected; completeness requires direct adjacency, not merely a connecting path.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Keller and Trotter — Applied Combinatorics (2016)Section 5.1, complete graph definition and notation K_n · Checked 2026-10-14

Translation sources

  1. 电子科技大学教学平台 — 《图论及其应用》习题课教材（片段）PDF pp.1–2，习题1，第2题与第6题「完全图」（名称证据） · Checked 2026-10-14
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