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Let $G = (V, E)$ be a graph, and $f: V \to \{1,-1\}$ be a function assigning a sign to each vertex. What is this system $(G, f)$ called?


  • In my current research, we've been using "oriented graph" to refer to the above structure; each vertex is assigned an orientation which is one of "oriented" or "unoriented". But other sources use "oriented graph" to mean a directed graph where there is at most one edge between a given pair of vertices.

  • A "signed graph" assigns $\pm 1$ to the edges, but not to the vertices.

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You might call it a vertex-signed graph. See e.g. this paper.

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