We claim that there is exactly one graph homomorphism \$$\alpha : G \rightarrow H \$$ such that \$$\alpha_{Arrow}(a) = d \$$.

1. What is the other value of \$$\alpha_{Arrow}\$$, and what are the three values of \$$\alpha_{Vertex} \$$?
2. Draw \$$\alpha_{Arrow} \$$ as two lines connecting the cells in the ID column of \$$G(Arrow)\$$ to those in the ID column of \$$H(Arrow)\$$. Similarly, draw \$$\alpha_{Vertex} \$$ as connecting lines.
3. Check the source column and target column and make sure that the matches are
natural, i.e. that “alpha-then-source equals source-then-alpha” and similarly for
“target”.

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$\begin{matrix} G := & & \begin{array}{c|cc} Arrow & source & target \\\\ \hline a & 1 & 2 \\\\ b & 2 & 3 \end{array} & & \begin{array}{c|} Vertex \\\\ \hline 1 \\\\ 2 \\\\ 3 \end{array} \\\\ H := & \begin{array}{c|cc} Arrow & source & target \\\\ \hline c & 4 & 5 \\\\ d & 4 & 5 \\\\ e & 5 & 5 \end{array} & & \begin{array}{c|} Vertex \\\\ \hline 4 \\\\ 5 \end{array} & \end{matrix}$