Graph Theory,

[acmzero]

Hi All, this is my first post, I'm not sure if this is the correct forum to post this question.

Basically I need to provide the steps to go from here:

(1/2) ( m[SUP]2[/SUP] + (v-2m)(v-m-1) + m(v-1))

To here:

C((v-1),2) +1 -(1/2)(m-1)(m-2) -(m-1)(v-2m-1)

Where C((v-1), 2) is the binomial coefficient of (v-1) choose 2.

I've tried to develop both expressions to see if I see common ground but it's helpless.

This is part of the proof of the Corollary 4.6 of the book "Graph Theory with Applications".

Any help or guidance will be much appreciated.

Thanks.

 

[tkhunny]

Hard to say where you're stuck. It's an algebra problem. Manipulate the symbols and see where it leads.

 

[acmzero]

Thanks for replying.

Hard to say where you're stuck. It's an algebra problem. Manipulate the symbols and see where it leads.

Well, I know I can rewrite

C((v-1), 2)

as

(1/2) (v-1) (v-2)

But still I can't get to the first form.

 

[tkhunny]

That's good. Seriously, this is kind of a silly exercise. I'm not sure of the rules of engagement. If it were me, I'd just expand both expressions and see if I get to the same place. This proves they are the same. It's quite possible that getting from one to the other takes some particularly unnatural steps.

 

[acmzero]

Just for the posterity, this is the solution to the problem.