Question textHow many edges end in a vertex of a 5D hypercube?Answer:Answer 1 Question 35[input]

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We’re dealing with a hypercube in 5 dimensions, often denoted as a 5D hypercube or Q5. A key property of an n-dimensional hypercube is that each vertex is connected to exactly n edges, corresponding to flipping each of the n coordinate bits once to reach a neighboring vertex. In more concrete terms, you can think of vertices as 5-bit binary strings; two vertices are adjacent if their strings differ in exactly one bit. For any given vertex, there are 5 possible single-bit changes, one for each dimension, which yields 5 neighboring vertices and thus 5 edges incident to that vertex. This aligns with the general rule that the degree of each vertex in an n-dimensional hypercube is n. Therefore, the number of edges that end in a vertex of a 5D hypercube corresponds to 5 possible incident edges per vertex.

MTH2132 - S1 2025 MTH2132 mock mid-semester test

Question textHow many edges end in a vertex of a 5D hypercube?Answer:Answer 1 Question 35[input]

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