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Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

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DM - Grand Test -Q4


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+1 vote

Let G=(V,E) be a graph. Define G^{-} to be (V,E^-), where for all u,v\in V(u,v)\in E^- if and only if (u,v)\notin E. Then which of the following is true ?

(A) G^- is always connected.

(B) G^- is connected only if G is not connected.

(C) At least one of G and G^- connected.

(D) G is not connected or G^- is not connected

asked Aug 30, 2020 by gbeditor-2 (72,840 points)
edited Sep 9, 2020 by deepak-gatebook

2 Answers

+2 votes
 
Best answer

Given definition is of complement of a graph 

A) it is false as if G is any complete graph  its complement will not be connected 

let us take the following graph which is connected  its complement will also be connected as below

B) complement of  G is connected if  G is not connected   so if G is not connected then its complement will be connected . so it is also true as at least one of them is always connected  ( had it been only if then it would have been false) 

C) is true as at least one of them ( one or both ) is always connected 

D)is false Here in above example  both are connected 

 

 

answered Sep 8, 2020 by (18,750 points)
selected Sep 9, 2020 by deepak-gatebook
Right. Have updated the options.
0 votes

imageSo we can observe that atleast one of them is connected. 

answered Sep 9, 2020 by deepak-gatebook (226,240 points)
Answer:

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