Automorphism I don't understand

Thread starter S&S
Start date Feb 20, 2006

AI Thread Summary

An automorphism of a graph G is defined as a permutation of its vertex set that preserves the edge structure, meaning that if {a,b} is an edge, then {p(a), p(b)} must also be an edge. This concept is closely related to isomorphisms, as an automorphism can be viewed as an isomorphism where the domain and codomain are the same graph. The discussion clarifies that while all automorphisms are isomorphisms, not all isomorphisms are automorphisms. Understanding this distinction is crucial for grasping the properties of graphs in mathematical contexts. The relationship between automorphisms and isomorphisms highlights the structural symmetries within graphs.

Feb 20, 2006

S&S

A permutation p of the vertex set of a graph G with the property that {a,b} is an edge if and only if {p(a), p(b)} is an dege, is called an automorphism of G. Is this right? this sounds isomorphism to me.

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Feb 20, 2006

AKG

Science Advisor

Homework Helper

An automorphism is an isomorphism whose domain equals its codomain. So you know the general notion of an isomorphism f : G -> H. Well an isomorphism f : G -> G is called an automorphism of G.

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