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+1 vote
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In a simple connected undirected graph with n nodes(where n≧2), The maximum number of nodes with distinct degrees is

  1.  n-1
  2. n-2
  3. n-3
  4. 2
asked in Algorithms by (51 points) 1 2 5 | 433 views

2 Answers

+4 votes

Answer will be (A)

for 3 nodes in a simple connected undirected graph degree can be 2,1,1

for 4 nodes in a simple connected undirected graph degree can be 3,2,2,1

By these degree we can draw a simple connected undirected graph (havel hakimi theorem)

 

 

answered by Veteran (64.8k points) 35 220 622
yes , u r right ..

for 5 nodes , I m getting degree sequence as 4,3,2,2,1

& for 6 nodes , as  5,4,3,3,2,1

But , Can u prove that given n vertices , we will always be able to form a simple,undirected, connected graph with n-1 distinct degrees ?
+1 vote
min degree of node is 1

max degree= n-1

so we have n vertices

2 vertices will have some degree acc to pigeon hole principle

so max no of nodes with distinct degree= n-1
answered by Veteran (32.9k points) 45 230 468


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