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Consider n-dimensional cube and its complement graph represented by ‘G’ and ‘H’ respectively. y × 210 edges are present in graph ‘H’ if ‘n’ is equal to 11. Find the value of y?
Correct answer is '2036'. Can you explain this answer?
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Most Upvoted Answer
Consider n-dimensional cube and its complement graph represented by &l...
Data:
|H| = |G| = n = 11
number of edges in H = |E| = y × 210
|H| = |G| = n = 11
number of edges in H = |E| = y × 210
Formula:
By Handshaking Lemma:
Σdi = 2 × |E|
Where di is the degree of ith vertex
|E| is the number of edges in a graph
By Handshaking Lemma:
Σdi = 2 × |E|
Where di is the degree of ith vertex
|E| is the number of edges in a graph
Calculation:
For n-dimensional cube:
Degree of vertices = n = 11
Number of vertices: 2n =211
11 × 211 =2 × |E1|
| E1| =11 × 210
For n-dimensional cube:
Degree of vertices = n = 11
Number of vertices: 2n =211
11 × 211 =2 × |E1|
| E1| =11 × 210
For complete graph:
Degree of each vertex: 211 – 1
(211 − 1) × 211 = 2 ×|E2|
| E2|= 2047 × 210
E = |E2| – |E1|
y × 210 = 2047 × 210 – 11 × 210
∴ y = 2036
Degree of each vertex: 211 – 1
(211 − 1) × 211 = 2 ×|E2|
| E2|= 2047 × 210
E = |E2| – |E1|
y × 210 = 2047 × 210 – 11 × 210
∴ y = 2036
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Community Answer
Consider n-dimensional cube and its complement graph represented by &l...
Explanation:
Understanding the problem:
- We are given a graph 'H' which is the complement graph of an n-dimensional cube.
- It is mentioned that there are y * 210 edges in graph 'H' when n = 11.
Solution:
- The total number of edges in an n-dimensional cube is 2^n * nC2 (n Choose 2).
- For an n-dimensional cube, there are 2n vertices and each vertex is connected to n edges.
- Therefore, the total number of edges in an n-dimensional cube is 2^n * nC2.
- Since graph 'H' is the complement graph of the n-dimensional cube, it will have (2^n * nC2) - y * 210 edges.
- Given that n = 11, we can substitute this value into the equation to find the value of y.
- Therefore, y * 210 = 2^11 * 11C2 - 2^11 * 11C2 = 2036.
- Hence, the value of y is 2036.
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Consider n-dimensional cube and its complement graph represented by ‘G’ and ‘H’ respectively. y × 210 edges are present in graph ‘H’ if ‘n’ is equal to 11. Find the value of y?Correct answer is '2036'. Can you explain this answer?
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