GATE CSE
First time here? Checkout the FAQ!
x
+9 votes
827 views

An undirected graph $G(V,E)$ contains $n \: (n>2)$ nodes named $v_1,v_2, \dots, v_n$. Two nodes $v_i, v_j$  are connected if and only if $ 0 < \mid i-j\mid \leq 2$. Each edge $(v_i,v_j)$ is assigned a weight $i+j$. A sample graph with $n=4$ is shown below.

The length of the path from $v_5$ to $v_6$ in the MST of previous question with $n=10$ is

  1. 11
  2. 25
  3. 31
  4. 41
asked in Algorithms by Veteran (92.5k points) 972 2329 3115 | 827 views
Its a linked question. Previous question is- http://gateoverflow.in/2162/gate2011-54

3 Answers

+7 votes
Best answer

Above is the graph....
Below is the MST.

Length of the path from v5 to v6= 8+4+3+6+10= 31 (Ans)

 

answered by Boss (7k points) 4 13 42
selected by
+6 votes

 

There is no direct edge between Vi and Vi+1 vertex in mst except V1 to V2 so path from Vi and Vi+1 includes all edges from v1 to Vi+1 which are in mst:

edge weights in mst:

=3 + 4 + 6 + 8 + 10 + 12 +...+*(2(n-1))

=1+(2+ 4+6+....till n-1 terms)

=1+ 2(1+2+3+4+...n-1) 

=1+(n-1)*n=n2-n+1

In this case v6 = 62-6+1 =31

 

answered by Veteran (25.3k points) 13 60 193
edited by
@Gabbar how u write equation??
kk i got it thks
@Gabbar , if we draw MST and find the value it will give 31 as answer

the weights are 4+3+6+8+10=31
@srestha there is 8 not 9 in MST...plz check it...

and 11 is not possible since it generates cycle...
yes.
+4 votes

Answer is C.

It can be easily obtained by drawing graph for up to 7 vertices.

answered by Loyal (4.1k points) 8 41 59
Answer is 31 but we have to draw 10 vertices to get it
Why isn't ans $11$ as there is a edge between vertex(5) and vertex(6) ?
because it create cycle by create minimum spaning tree.
No, 7 vertices are sufficient to calculate cost of 5-6.
Draw spanning tree upto 7 vertices, then you will see if v5 to v6 length is 11 and we add that then that will create a cycle.

NO need to draw full spanning tree..

there is no direct edge between Vi and Vi+1 vertex so path from Vi and Vi+1 includes all edges from v1 to Vi+1 which are in mst:

equation: n2-n + 1 from previous question

in our case v6 = 62-6+1 =31

Answer:

Related questions



Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
Top Users Oct 2017
  1. Arjun

    23398 Points

  2. Bikram

    17078 Points

  3. Habibkhan

    8280 Points

  4. srestha

    6300 Points

  5. Debashish Deka

    5438 Points

  6. jothee

    4978 Points

  7. Sachin Mittal 1

    4772 Points

  8. joshi_nitish

    4352 Points

  9. sushmita

    3970 Points

  10. Rishi yadav

    3804 Points


Recent Badges

Popular Question sh!va
Popular Question sh!va
Regular Rishabh Gupta 2
Popular Question Sunil8860
Reader Rajesh Veeranki 2
Notable Question rahul sharma 5
Commentator Shivam Chauhan
Notable Question set2018
Nice Comment srestha
Notable Question set2018
27,325 questions
35,177 answers
84,124 comments
33,280 users