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@TuringTest @amistre64 @satellite73
That's like the easiest graph question in the book
or n vertices
Here's a counter example: |dw:1332548723247:dw|
4 vertices, 6 edges
hmm where did u get that from?
From my head
No I need reasoning I don't just want the answer, any steps?
Yeah, it's called trial and error
Start with a graph of three edges, and then test using that. Then keep going until you find the pattern.
wait what's n? Number of edges?
Then n(n-1)/2 doesn't work, the graph above has 6 edges, then according to u it must have: 6*5/2=15 vertices
I thought for sure the answer was one of those.
Hmm I'm not sure if amistre got a notification: @amistre64
@radar any ideas how to do this?
i got notifed but was buzy in a prior question
None. Was hoping someone had it.
It can't be that difficult
oh yes it is lol this is graph theory
I was just doing this not too long ago. It's not that difficult
It can get very nasty.. actually the original question asked: Let G be a connected graph with 66 edges. How many vertices can G have?
I apparently have forgotten the answer to the general question
Let G be a connected regular graph with n edges. How many vertices can G have? vertices are the nodes, dots, point along the way?
Yea: |dw:1332550157890:dw| Those dots are vertices
and the edges are?
edges are the lines.. wait let me find what connected means, i forgot
|dw:1332550278092:dw| 3 edges 4 verts; but i doubt this passes the connected definition
No i think connected means there's a vertex between any two edges.. but that could have meant complete, ughh too many definitions in graph theory.
amistre, your graph isn't "connected". What you have posted is a "tree"
Use Hero's n(n-1)/2 where n is number of vertices (not edges)
http://mathworld.wolfram.com/RegularGraph.html M=1/2 nr where M = number of edges, n = number of nodes, and r = something regular :)
trees are graphs i thought
There is a path between any two points, so amistre's tree is in fact connected, I can find a path between any two points.
Every pair of vertices is connected by a unique edge.
Wait merts I think that's the definition of a complete graph
According to wolf: http://mathworld.wolfram.com/ConnectedGraph.html A graph which is connected in the sense of a topological space, i.e., there is a path from any point to any other point in the graph.
What I meant to say was that the graph wasn't "complete" like bahrom said.
I haven't dealt with graph theory in a while
integrals a pirate lol
i got like all legends on my question.. lol
Yes but we need Satellite
I don't feel so bad now
I know, I reposted... I hate this class... crap.. just wanna swear so bad lol
I told you to use trial and error
I think it's n+1
Start with a complete graph of 3 vertices, then 4, then 5, and then keep going until you have a decent amount. You are bound to find the pattern
No, not complete, connected.
Do you have a list of answers from which to choose?
No lol and I have to write some reasoning for this.
3 edges can have at most 4 verts and at least 3 verts
I finally found it. A tree with n vertices, has exactly n - 1 edges. So it looks like you were right.
6es can have at least 4 verts, and at most 7 verts
So integral found the answer to his own question and mertsj gave the visual presentation. and like I said, It was easy. I just couldn't produce the results quickly enough. I hate graph theory as much as you do integral.
Good luck with your reasoning
Wait the key point was regular.. Regular means each vertex has the same number of edges coming out of it. So the answer must be n
Don't tell me you're going back to the very first answer I supplied
well one of them at least
dude random guesses don't work here lol, I gotta prove this now
Yes, it is important to specify whether you're dealing with a tree, a regular, or a complete graph.
Maybe that would explain my "randomness"
Maybe reading the question would help? I specified that G was a connected regular graph lol
I skipped right over the word "regular" Didn't even see it. My apologies
I tend to do that sometimes.
Here's what I thought I was reading the first time : "Let G be a connected graph with n edges. How many vertices can G have?" I feel that the confusion was all my fault.