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Let G be the graph with 100 vertices numbered 1 to 100. Two vertices i and j are adjacent iff |i−j|=8 or |i−j|=12. The number of connected components in G is
- a)8
- b)4
- c)12
- d)25
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Let G be the graph with 100 vertices numbered 1 to 100. Two vertices i...
When vertices are arranged with difference of 8 there are 8 components as shown by 8 columns in the image below:
When vertices are arranged withdifference of 12 the number of components is reduced to 4 as first column will be connected with fifth column, second column will be connected with sixth column, third column will be connected with seventh column and fourth column will be connected with eighth column. No other form of connection exists so total 4 connected components are there. So, option (B) is correct. This explanation is contributed by Pradeep Pandey.
Most Upvoted Answer
Let G be the graph with 100 vertices numbered 1 to 100. Two vertices i...
The graph G has 100 vertices numbered from 1 to 100. Two vertices i and j are adjacent if and only if |i-j| ≤ 5.
To find the number of edges in this graph, we need to count the number of pairs of adjacent vertices.
For any vertex i, there are 10 vertices (i-5, i-4, ..., i-1, i+1, ..., i+5) that are adjacent to it. However, we need to consider the cases where i ≤ 5 or i ≥ 96 separately, since there will be fewer adjacent vertices for these vertices.
For i ≤ 5, there are only 5 adjacent vertices (i+1, i+2, i+3, i+4, i+5).
For i ≥ 96, there are only 5 adjacent vertices (i-1, i-2, i-3, i-4, i-5).
For the remaining vertices 6 ≤ i ≤ 95, there are 10 adjacent vertices.
So, the total number of edges in the graph G is:
(5 vertices with 5 adjacent vertices) + (90 vertices with 10 adjacent vertices) + (5 vertices with 5 adjacent vertices) = 5*5 + 90*10 + 5*5 = 25 + 900 + 25 = 950.
Therefore, the graph G has 950 edges.
To find the number of edges in this graph, we need to count the number of pairs of adjacent vertices.
For any vertex i, there are 10 vertices (i-5, i-4, ..., i-1, i+1, ..., i+5) that are adjacent to it. However, we need to consider the cases where i ≤ 5 or i ≥ 96 separately, since there will be fewer adjacent vertices for these vertices.
For i ≤ 5, there are only 5 adjacent vertices (i+1, i+2, i+3, i+4, i+5).
For i ≥ 96, there are only 5 adjacent vertices (i-1, i-2, i-3, i-4, i-5).
For the remaining vertices 6 ≤ i ≤ 95, there are 10 adjacent vertices.
So, the total number of edges in the graph G is:
(5 vertices with 5 adjacent vertices) + (90 vertices with 10 adjacent vertices) + (5 vertices with 5 adjacent vertices) = 5*5 + 90*10 + 5*5 = 25 + 900 + 25 = 950.
Therefore, the graph G has 950 edges.
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Let G be the graph with 100 vertices numbered 1 to 100. Two vertices i and j are adjacent iff |i−j|=8 or |i−j|=12. The number of connected components in G isa)8b)4c)12d)25Correct answer is option 'B'. Can you explain this answer?
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