Decidability one relation, binary FOL over finite models

Suppose $\sigma$ is a vocabulary consisting of one binary relation $E$ and let $\phi$ be a $\sigma$ sentence. Is it decidable whether there is a finite directed graph $G$, with all in- and out-degrees $0$ or $1$, such that $G\models \phi$ ?

• This is a very elementary question, and not of the level usually answered here. Read any basic text on Finite Model Theory and you should know the answer. – Marc Hamann Mar 10 '13 at 15:44
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