

Subject:
TREES AND GRAPHS
Category: Computers > Algorithms Asked by: dan1976ga List Price: $3.00 
Posted:
25 Apr 2005 22:07 PDT
Expires: 25 May 2005 22:07 PDT Question ID: 514258 
1) If a forest F consists of m trees and has n vertices, how many edges does F have.?  


There is no answer at this time. 

Subject:
Re: TREES AND GRAPHS
From: quadraticresiduega on 26 Apr 2005 09:08 PDT 
If you try a few examples, you should be able to see a pattern pretty easily. 
Subject:
Re: TREES AND GRAPHS
From: mathtalkga on 27 Apr 2005 06:53 PDT 
What a great handle, "quadraticresiduega"! Yes, start with a single tree. If it had n vertices, it would have n1 edges. Now a forest is a collection of trees. In each tree there is one fewer edge than the number of vertices in that tree. So, how many edges does a forest F require with m trees and n vertices (total)? regards, mathtalkga 
Subject:
Re: TREES AND GRAPHS
From: dikunga on 02 May 2005 12:38 PDT 
Sorry for my broken English! > If a forest F consists of m trees and has n vertices, how many edges does F have.? > F is simpe graph with no cycles For all trees Ti from the forest F (1 <= i <= m): V(Ti) = Vi  a quantity of vertices, 1 <= i <= m. E(Ti) = Ei  a quantity of edges, 1 <= i <= m. Ei = Vi  1  this is a simple feature of tree. E(F) = E1 + E2 + ... + Em = (V1  1) + (V2  1) + ... + (Vm  1) = (V1 + V2 + ... + Vm)  m. But V1 + V2 + ... + Vm = V(F) = n. Then E(F) = n  m. Thanx. 
Subject:
Re: TREES AND GRAPHS
From: abdulmuqsithga on 26 Aug 2005 07:18 PDT 
Forest if collection of disjoint trees. Step 1: Start from a single tree with n vertices. This will have n1 edges. Step 2: Remove an edge from this tree. Now there are 2 trees and number of edges = n2. Step 3: Recursively going the Step 2 m1 times will leave us with m trees and number of edges = nm. 
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