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Graph theoretical questions with a topological flavour. For example, graphs on surfaces, spatial embeddings, and geometric graphs. Use the graph-drawing tag for questions specific to graph drawing (e.g. crossing numbers).
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Gauss-Bonnet Theorem for Graphs?
One can define the Euler characteristic χ for a graph as the number of vertices minus the number of edges. Thus an $n$-cycle has $\chi = 0$ and $K_4$ has $\chi=-2$.
Is there an analog for the Gaus …