Orthogonal embeddings of graphs in Euclidean space
Let G = (V, E) be a simple connected graph. An injective function f : V → Rn is called an n-dimensional (or n-D) orthogonal labeling of G if uv, uw ∈ E implies that (f(v) − f(u)) ⋅ (f(w) − f(u)) = 0, where ⋅ is the usual dot product in Euclidean space. If such an orthogonal labeling f of G exists,...
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GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,
2019-10-10.
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