First time here? Checkout the FAQ!
+1 vote

Let A has n vertices. If Ā is connected graph then the maximum number of edges that A can have is

a) (n-1)(n-2)/2
b) n(n-1)/2
c) n-1
d) n

asked in Mathematical Logic by Junior (919 points)   | 116 views

I am getting option a , but by substitution , what is the standard way to solve it. I solve it for n=3,4 ,5 and got option a

think like ...

you have a grapg A with n vertices.  excepts one vertex, all n-1 vertices are making a complete graph with total

(n-1)(n-2)/2 edges. Now if we see complement of this graph then it would be connected right ( A' ->star graph)??

And if we add any more edge in A,  then it would make its complement disconnected ...

Note-  we are not told that A is also connected.. only A' is connected.

just give it  think ..

1 Answer

+2 votes
Best answer
If  $A^c$   is connected then minimum no. of  edges in $A^c$   are n-1

so  maximum no. of edges in A= Total edges - minimum edges in $A^c$

= $_{2}^{n}\textrm{c}$ - (n-1)

=n(n-1)/2 -(n-1)


option A)
answered by Loyal (3.8k points)  
selected by
option A is correct.

Top Users Mar 2017
  1. rude

    4768 Points

  2. sh!va

    3054 Points

  3. Rahul Jain25

    2920 Points

  4. Kapil

    2734 Points

  5. Debashish Deka

    2592 Points

  6. 2018

    1544 Points

  7. Vignesh Sekar

    1422 Points

  8. Akriti sood

    1342 Points

  9. Bikram

    1312 Points

  10. Sanjay Sharma

    1126 Points

Monthly Topper: Rs. 500 gift card

21,508 questions
26,832 answers
23,146 users