Automorphism Of A Colored Directed Graph

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Definition (Automorphism Of A Colored Directed Graph)

Let $\mathcal{G}=(V,C,A)$ be a colored directed graph, where the vertex set is $V$ and the list of colored arrows is $A$, where each arrow in the list $A$ is assigned a unique color from $C$. An automorphism of a directed colored graph is a permutation $\sigma:V\to V$ of the vertex set such that $(x,y)$ is an arrow colored $c\in C$ if and only if $(\sigma(x),\sigma(y))$ is an arrow colored $c$. In other words, it's a permutation of $H$ that preserves the arrow and color structure of the graph.

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