k-regular graph
Set
| context | n∈N,n≥1 |
| definiendum | Qn≡⟨V,E⟩ |
| postulate | V={0,1}n |
| for all | v,w∈V |
| range | k∈N,1≤k≠n |
| postulate | {v,w}∈E↔∃!k. πk(v)≠πk(w) |
Discussion
The n-cube Qn is the graph with vertices being n-tuples which are connected exactly if they differ by one coordinate.
Examples
V(Q2)={⟨0,0⟩,⟨0,1⟩,⟨1,0⟩,⟨1,1⟩}
E(Q2)={{⟨0,0⟩,⟨0,1⟩},{⟨0,0⟩,⟨1,0⟩},{⟨0,1⟩,⟨1,1⟩},{⟨1,0⟩,⟨1,1⟩}}
… that's a square.
Parents
Subset of
Context
