Isomorphism:
From Theoretical Biology, isomorphy is seen as a similarity of shape, structure or form. This website is designed to describe some of the more technical aspects of isomorphism.
For a less complex description, please feel free to see http://isomorphy.bravehost.com
Lindblom
For a complex description, please see:
What is it?
"The word derives from the Greek iso, meaning "equal," and morphosis, meaning "to form" or "to shape."
Formally, an isomorphism is bijective morphism. Informally, an isomorphism is a map that preserves sets and relations among elements.
http://mathworld.wolfram.com/Isomorphism.html
Please note that the word "equal" may mean equivalent in some cases.
Lindblom
In mathematics, an isomorphism (Greek:isos "equal", and morphe "shape") is a bijective map f such that both f and its inverse f −1 are homomorphisms, i.e. structure-preserving mappings.
Informally, an isomorphism is a kind of mapping between objects, which shows a relationship between two properties or operations.
http://en.wikipedia.org/wiki/Isomorphism
An Example
Graph isomorphism:
A graph isomorphism is a bijection between the vertices of two graphs 
and 
:
with the property that any two vertices 
and 
from 
are adjacent if and only if 
and 
are adjacent in 
.
If an isomorphism can be constructed between two graphs, then we say those graphs are isomorphic.
For example, consider these two graphs:
More?
http://planetmath.org/encyclopedia/GraphIsomorphism.html
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