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How to judge whether two are isomorphic?
1. A one-to-one mapping can be established between the vertex sets of two graphs, and the corresponding vertices maintain the one-to-one correspondence of edges.

2. It can also be discussed through the adjacency matrix of graphs. If the adjacency matrix of one graph is transformed into the adjacency matrix of another graph through a finite number of row or column exchanges, then the two graphs are isomorphic.

Isomorphism is a kind of mapping defined between mathematical objects, which can reveal the relationship between the attributes or operations of these objects. If there is isomorphic mapping between two mathematical structures, then the two structures are called isomorphic.

Generally speaking, if the specific definitions of the properties or operations of homogeneous objects are ignored, homogeneous objects are completely equivalent only in terms of structure.

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purpose

The main purpose of studying isomorphism in mathematics is to apply mathematical theory to different fields. If two structures are isomorphic, the objects above them will have similar properties and operations, and the proposition that holds for one structure also holds for the other structure.

Therefore, if an object structure is found to be isomorphic to a structure in a certain mathematical field, and many theorems have been proved for this structure, then these theorems can be applied to this field immediately.

If some mathematical methods can be used in this structure, then these methods can also be used in the structure of new fields. This makes it easy to understand and deal with the structure of objects, and often makes mathematicians have a deeper understanding of this field.

Baidu encyclopedia-isomorphism