A community for students.
Here's the question you clicked on:
 0 viewing
prizzyjade
 one year ago
A simple graph that is isomorphic to its complement is self complementary.
a. Prove that if G is self complementary, then G has 4k or 4k+1 vertices where k is an integer.
prizzyjade
 one year ago
A simple graph that is isomorphic to its complement is self complementary. a. Prove that if G is self complementary, then G has 4k or 4k+1 vertices where k is an integer.

This Question is Closed

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1The statement should include \(4k\) not just\(4k+1\) (look at part b) The complete graph with \(n\) vertices has \(\frac{1}{2}n(n1)\) edges. Why? Because for each of the \(n\) vertices, there is \(n1\) edges, but we count them all twice. If a graph is self complimentary there must be \(\frac{1}{2}(\frac{1}{2}n(n1))\) edges because the compliment must have equal amount of edges. Now if \(\frac{1}{4}n(n1)\in \mathbb{Z}\) then it must be that \(4\) divides \(n(n1)\). In other words \(n=4k\) or \(n=4k+1\)

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1b) there is one self complimentary graph on 4 verts. Hint: it is super easy and I must draw the LINE at how much i will give.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1For 5 verts. I am sure that if you CYCLE through all the graphs you have in your wheel HOUSE I bet you will find it.

prizzyjade
 one year ago
Best ResponseYou've already chosen the best response.0Im Sorry.for not replying I still have class sorry

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1no problem. Class is important :)

prizzyjade
 one year ago
Best ResponseYou've already chosen the best response.0thanks for the help ....

prizzyjade
 one year ago
Best ResponseYou've already chosen the best response.0I'm having a hard time analyzing the problems coz i cant focus having so many math subjects ..

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1what all are you taking?

prizzyjade
 one year ago
Best ResponseYou've already chosen the best response.0Calculus with analytic geometry ,physics(i know its science but still it uses math ) and graph theory...

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.1yep, that is a full boat
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.