isomorfismiin

Isomorfism is a concept in mathematics and computer science that describes a relationship between two mathematical structures of the same type. These structures can be sets, groups, rings, graphs, or other mathematical objects. Two structures are said to be isomorphic if there exists a bijective function (a one-to-one correspondence) between their elements that preserves the structure's operations or relationships.

In the context of graph theory, for example, two graphs are isomorphic if there is a way to relabel the vertices of one graph to make it identical to the other graph. This means that the adjacency relationships between vertices are preserved under the relabeling.

Isomorphism is an equivalence relation, meaning it is reflexive, symmetric, and transitive. If two structures are isomorphic, they are considered essentially the same for most practical purposes, as any property or behavior that holds in one structure will also hold in the other.

Isomorphisms are used in various areas of mathematics and computer science, including group theory, ring theory, graph theory, and cryptography. They provide a way to study the underlying structure of mathematical objects without being concerned with the specific details of their representation.