Question

1. How many nodes does a d-dimensional hypercube has, as a function of dimension?

2. How many edges does a d-dimensional hypercube has, as a function of dimension?

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Answer 1

1. How many nodes does a d-dimensional hypercube has, as a function of dimension?

The number of nodes in d-dimensional hypercube is 2^d.

If the hypercube is one dimensional no of nodes(vertices)=2^1=2

Two dimensional no of nodes =2^2=4

3 dimensional no of nodes =2^3=8 and so on.....

2. How many edges does a d-dimensional hypercube has, as a function of dimension?

The no of edges =d * 2^d-1

If it is one dimension no of edges = 1*2^1-1=1*2^0 =1

2-dimensional no of edges =2* 2^2-1 = 2*2 =4

And so on....

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