Question

Let G = (V,E) be a graph with n vertices and e edges. Show that the...

Let G = (V,E) be a graph with n vertices and e edges. Show that the following statements are equivalent:

1. G is a tree

2. G is connected and n = e + 1

3. G has no cycles and n = e + 1

4. If u and v are vertices in G, then there exists a unique path connecting u and v.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
30. a) Show if G is a connected planar simple graph with v vertices and e...
30. a) Show if G is a connected planar simple graph with v vertices and e edges with v ≥ 3 then e ≤ 3v−6. b) Further show if G has no circuits of length 3 then e ≤ 2v−4.
A spanning tree of connected graph G = (V, E) is an acyclic connected subgraph (V,...
A spanning tree of connected graph G = (V, E) is an acyclic connected subgraph (V, E0 ) with the same vertices as G. Show that every connected graph G = (V, E) contains a spanning tree. (It is the connected subgraph (V, E0 ) with the smallest number of edges.)
Let G be an undirected graph with n vertices and m edges. Use a contradiction argument...
Let G be an undirected graph with n vertices and m edges. Use a contradiction argument to prove that if m<n−1, then G is not connected
In lecture, we proved that any tree with n vertices must have n − 1 edges....
In lecture, we proved that any tree with n vertices must have n − 1 edges. Here, you will prove the converse of this statement. Prove that if G = (V, E) is a connected graph such that |E| = |V| − 1, then G is a tree.
Let G be the graph having 3 vertices A, B and C. There are five edges...
Let G be the graph having 3 vertices A, B and C. There are five edges connecting A and B and three edges connecting B and C. Solve the following: 1) Determine the number of paths from A to B 2) Determine the number of different trails of length 6 from A to B
Graph Theory . While it has been proved that any tree with n vertices must have...
Graph Theory . While it has been proved that any tree with n vertices must have n − 1 edges. Here, you will prove the converse of this statement. Prove that if G = (V, E) is a connected graph such that |E| = |V | − 1, then G is a tree.
Let G be a connected simple graph with n vertices and m edges. Prove that G...
Let G be a connected simple graph with n vertices and m edges. Prove that G contains at least m−n+ 1 different subgraphs which are polygons (=circuits). Note: Different polygons can have edges in common. For instance, a square with a diagonal edge has three different polygons (the square and two different triangles) even though every pair of polygons have at least one edge in common.
Let G=(V,E) be a connected graph with |V|≥2 Prove that ∀e∈E the graph G∖e=(V,E∖{e}) is disconnected,...
Let G=(V,E) be a connected graph with |V|≥2 Prove that ∀e∈E the graph G∖e=(V,E∖{e}) is disconnected, then G is a tree.
Let u and v be distinct vertices in a graph G. Prove that there is a...
Let u and v be distinct vertices in a graph G. Prove that there is a walk from ? to ? if and only if there is a path from ? to ?.
Show that if G is connected with n ≥ 2 vertices and n − 1 edges...
Show that if G is connected with n ≥ 2 vertices and n − 1 edges that G contains a vertex of degree 1. Hint: use the fact that deg(v1) + ... + deg(vn) = 2e
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT