---
tag: 70XS2M1FWW
kind: concept
name: Homomorphic equivalence
aliases: [homomorphically-equivalent]
sources:
  - wikipedia: en:51231053@r1240292381
    locator: Homomorphic equivalence
    note: adopted
    mention: wikipedia://en/51231053
    sections: [Summary]
same_as:
  wikidata: Q28402047
  wikipedia: Homomorphic equivalence
inventory: [K0T8VMFC7S]
---

## Summary

In graph theory, a branch of mathematics, two graphs *G* and *H* are called **homomorphically equivalent** if there exists a [[graph homomorphism|052JJ9YVNM]] $f\colon G \to H$ and a graph homomorphism $g\colon H \to G$. An example usage of this notion is that any two cores of a graph are homomorphically equivalent.