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I have the following (directed) graph:

A --> B

the transition is labled C. Is there symbol to denote the inverse of the (A,B) transtion?

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Did you mean in a en.wikipedia.org/wiki/State_transition_system labelled transition system”? –  beroal Feb 28 '11 at 12:17
    
I'm not aware of any standard notation, you can just invent one. –  Yuval Filmus Feb 28 '11 at 14:06
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1 Answer 1

As Yuval mentioned there's no direct simple standard notation. But:

  • a directed graph is a relation, and this an be represented by a square adjacency matrix $A$, so the graph with all edges reversed has the transposed adjacency matrix $A^T$.

  • in category theory, for a given category $C$, the same objects and the reverse of all arrows as $C$ is called $C^{op}$.

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