---
tag: 3E80DQEDKV
kind: concept
name: Fan graph
sources:
  - wikipedia: en:81762753@r1326288613
    locator: Fan graph
    note: adopted
    mention: wikipedia://en/81762753
    sections: [Summary]
same_as:
  wikidata: Q128818074
  wikipedia: Fan graph
inventory: [B6D7EPKFA7]
---

## Summary

In graph theory, a **fan graph** (also called a path-fan graph) is a graph formed by the join of a [[path graph|075WR6W3Y3]] and an empty graph on a single vertex. The fan graph on $n + 1$ vertices, denoted $F_n$, is defined as $K_1 + P_n$, where $K_1$ is a single vertex and $P_n$ is a path on $n$ vertices.