---
tag: PY7DPX0K9B
kind: concept
name: Bipartite half
aliases: [half-square]
sources:
  - wikipedia: en:39329230@r1352460392
    locator: Bipartite half
    note: adopted
    mention: wikipedia://en/39329230
    sections: [Summary]
same_as:
  wikidata: Q17005048
  wikipedia: Bipartite half
inventory: [J9P88MR9W6]
---

## Summary

In graph theory, the **bipartite half** or **half-square** of a [[bipartite graph|07DVHJ8N0A]] $G = (U,V,E)$ is a [[graph|00C0BR7D7H]] whose vertex set is one of the two sides of the bipartition (without loss of generality, $U$) and in which there is an edge $u_{i}u_{j}$ for each pair of vertices $u_{i}, u_{j}$ in $U$ that are at [[distance|0QV9VNNB4Z]] two from each other in $G$. That is, in a more compact notation, the bipartite half is $G^{2}[U]$ where the superscript 2 denotes the square of a graph and the square brackets denote an [[induced subgraph|0EREPBVG2G]].