---
tag: BJTMQKXV5D
kind: concept
name: Universal vertex
aliases: [cone-graph-theory, dominating-vertex]
sources:
  - wikipedia: en:51352780@r1290629220
    locator: Universal vertex
    note: adopted
    mention: wikipedia://en/51352780
    sections: [Summary]
same_as:
  wikidata: Q26789594
  wikipedia: Universal vertex
inventory: [WMTVHDMHV2]
---

## Summary

In graph theory, a **universal vertex** is a vertex of an undirected graph that is adjacent to all other vertices of the graph. It may also be called a **dominating vertex**, as it forms a one-element dominating set in the graph. A graph that contains a universal vertex may be called a **cone**, and its universal vertex may be called the **apex** of the cone. This terminology should be distinguished from the unrelated usage of these words for universal quantifiers in the logic of graphs, and for apex graphs.