Question

If G is an n-vertex r-regular graph, then show that n/(1+r)≤ α(G) ≤n/2.

If G is an n-vertex r-regular graph, then show that n/(1+r)≤ α(G) ≤n/2.

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 an n-vertex graph with n ≥ 2 and δ(G) ≥ (n-1)/2. Prove that...
Let G be an n-vertex graph with n ≥ 2 and δ(G) ≥ (n-1)/2. Prove that G is connected and that the diameter of G is at most two.
a graph is regular of degree k if every vertex has the same degree, k. show...
a graph is regular of degree k if every vertex has the same degree, k. show that G has a hamiltonian circuit if G has 13 vertices and is regular of degree 6.
Let G be a graph or order n with independence number α(G) = 2. (a) Prove...
Let G be a graph or order n with independence number α(G) = 2. (a) Prove that if G is disconnected, then G contains K⌈ n/2 ⌉ as a subgraph. (b) Prove that if G is connected, then G contains a path (u, v, w) such that uw /∈ E(G) and every vertex in G − {u, v, w} is adjacent to either u or w (or both).
Prove the following bound for the independence number. If G is a n-vertex graph with e...
Prove the following bound for the independence number. If G is a n-vertex graph with e edges and maximum degree ∆ > 0, then α(G) ≤ n − e/∆.
a. A graph is called k-regular if every vertex has degree k. Explain why any k-regular...
a. A graph is called k-regular if every vertex has degree k. Explain why any k-regular graph with 11 vertices must conain an Euler circuit. (Hint – think of the possible values of k). b. If G is a 6-regular graph, what is the chromatic number of G? Must it be 6? Explain
A K-regular graph G is a graph such that deg(v) = K for all vertices v...
A K-regular graph G is a graph such that deg(v) = K for all vertices v in G. For example, c_9 is a 2-regular graph, because every vertex has degree 2. For some K greater than or equal to 2, neatly draw a simple K-regular graph that has a bridge. If it is impossible, prove why.
Let G be a graph with vertex set V. Define a relation R from V to...
Let G be a graph with vertex set V. Define a relation R from V to itself as follows: vertex u has this relation R with vertex v, u R v, if there is a path in G from u to v. Prove that this relation is an equivalence relation. Write your proof with complete sentences line by line in a logical order.  If you can, you may write your answer to this question directly in the space provided.Your presentation counts.
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
Show that if G is a graph with n ≥ 2 vertices then G has two...
Show that if G is a graph with n ≥ 2 vertices then G has two vertices with the same degree.
let G be a connected graph such that the graph formed by removing vertex x from...
let G be a connected graph such that the graph formed by removing vertex x from G is disconnected for all but exactly 2 vertices of G. Prove that G must be a path.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT