Question

let a be a positive integer. Is it possible to have a graph with degrees 1,...

let a be a positive integer. Is it possible to have a graph with degrees 1, 2, 3... 4a + 1 if the graph has 4a + 1 vertices

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 n be a positive integer, and let Hn denote the graph whose vertex set is...
Let n be a positive integer, and let Hn denote the graph whose vertex set is the set of all n-tuples with coordinates in {0, 1}, such that vertices u and v are adjacent if and only if they differ in one position. For example, if n = 3, then (0, 0, 1) and (0, 1, 1) are adjacent, but (0, 0, 0) and (0, 1, 1) are not. Answer the following with brief justification (formal proofs not necessary): a....
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.)
Let ? be a graph and let ? be a subgraph of ?. Assume ? contains...
Let ? be a graph and let ? be a subgraph of ?. Assume ? contains at least three vertices. a) Is it possible for ? to be bipartite and for ? to be a complete graph? b) Is it possible for ? to be a complete graph and for ? to be bipartite?
Prove that every graph has two vertices with the same degree. (hint: what are the possible...
Prove that every graph has two vertices with the same degree. (hint: what are the possible degrees?)
Let m be a composite positive integer and suppose that m = 4k + 3 for...
Let m be a composite positive integer and suppose that m = 4k + 3 for some integer k. If m = ab for some integers a and b, then a = 4l + 3 for some integer l or b = 4l + 3 for some integer l. 1. Write the set up for a proof by contradiction. 2. Write out a careful proof of the assertion by the method of contradiction.
Let p be an odd prime and let a be an odd integer with p not...
Let p be an odd prime and let a be an odd integer with p not divisible by a. Suppose that p = 4a + n2 for some integer n. Prove that the Legendre symbol (a/p) equals 1.
Let G be a simple graph in which all vertices have degree four. Prove that it...
Let G be a simple graph in which all vertices have degree four. Prove that it is possible to color the edges of G orange or blue so that each vertex is adjacent to two orange edges and two blue edges. Hint: The graph G has a closed Eulerian walk. Walk along it and color the edges alternately orange and blue.
Let n be a positive integer and let S be a subset of n+1 elements of...
Let n be a positive integer and let S be a subset of n+1 elements of the set {1,2,3,...,2n}.Show that (a) There exist two elements of S that are relatively prime, and (b) There exist two elements of S, one of which divides the other.
Let λ be a positive irrational real number. If n is a positive integer, choose by...
Let λ be a positive irrational real number. If n is a positive integer, choose by the Archimedean Property an integer k such that kλ ≤ n < (k + 1)λ. Let φ(n) = n − kλ. Prove that the set of all φ(n), n > 0, is dense in the interval [0, λ]. (Hint: Examine the proof of the density of the rationals in the reals.)
Very confused about where to place vertices in the graph according to their the degrees so...
Very confused about where to place vertices in the graph according to their the degrees so I can find the edge set... Construct a simple graph with vertices O,P,Q,R,S,T whose degrees are 4, 3, 4, 4, 1, 4 What is the edge set?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT