Question

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

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
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 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.
A simple undirected graph consists of n vertices in a single component. What is the maximum...
A simple undirected graph consists of n vertices in a single component. What is the maximum possible number of edges it could have? What is the minimum possible number of edges it could have? Prove that your answers are correct
Let n be a positive integer and G a simple graph of 4n vertices, each with...
Let n be a positive integer and G a simple graph of 4n vertices, each with degree 2n. Show that G has an Euler circuit. (Hint: Show that G is connected by assuming otherwise and look at a small connected component to derive a contradiction.)
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 there be planar graph G with 12 vertices where every vertices may or may not...
Let there be planar graph G with 12 vertices where every vertices may or may not be connected by an edge. The edges in G cannot intersect. What is the maximum number of edges in G. Draw an example of G. What do you notice about the faces and the maximum number of edges?
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
Call a graph on n vertices dendroid if it has n edges and is connected. Characterize...
Call a graph on n vertices dendroid if it has n edges and is connected. Characterize degree sequences of dendroids.
Suppose G is a simple, nonconnected graph with n vertices that is maximal with respect to...
Suppose G is a simple, nonconnected graph with n vertices that is maximal with respect to these properties. That is, if you tried to make a larger graph in which G is a subgraph, this larger graph will lose at least one of the properties (a) simple, (b) nonconnected, or (c) has n vertices. What does being maximal with respect to these properties imply about G?G? That is, what further properties must GG possess because of this assumption? In this...
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.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT