finite simple graph

简单图

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

Other names / variants: simple undirected graph

Translation evidence: Literature usage

Meaning in context

A finite simple graph is a pair (V,E) with V finite and E a set of two-element subsets of V; edges are undirected, with no loops or repetitions.

有限简单图由有限顶点集 V 和二元子集构成的边集 E 组成；边无方向，不允许自环和重边。

Example

$V=\{a,b,c\}$ and $E=\{\{a,b\},\{b,c\}\}$ define a simple graph.

Usage and distinctions

Drawing crossings are not vertices unless included in V; parallel routes require a multigraph if their identities matter.

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Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Keller and Trotter — Applied Combinatorics (2016)Section 5.1, graph/degree/subgraph/path/cycle/isomorphism/tree definitions; Theorem 5.9 · Checked 2026-10-14

Translation sources

1. 新疆大学 — 本科课程教学大纲汇编，图论（050762）PDF pp.94–95，图论课程四、第一部分，教学目的「简单图」及第一章「图与子图」 · Checked 2026-10-14

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