(5pts) Clearly state for what values of n ≥ 1 is there a simple 3-regular graph...
(5pts) Clearly state for what values of n ≥ 1 is there a simple 3-regular graph with n vertices.
For those values of n for which you claimed that there is no simple 3-regular graph with n vertices, prove your claim.
(c) (10pts) For those values of n for which you claimed that there is a simple 3-regular graph with n vertices, describe it. You will have to describe an infinite family of graphs. You can use graphs that we defined in class as building blocks.
Homework Answers
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(5pts) Clearly state for what values of n ≥ 1 is there a simple
3-regular graph...
Graph theory a) prove that there is a 3 regular graph if n is even and...
Graph theory
a) prove that there is a 3 regular graph if n is even and
n>=4
b)
thank you
Exercise 4. How many distinct graphs are there with vertex set {1,2,...,n}? How many distinct graphs are there with vertex set {1,2,...,n} and m edges? For these questions, what happens if "with vertex set {1,2,...,n}" is replaced by "with n vertices"?
1: EDGES OF THE BIPARTITE GRAPH Please select file(s) Select image(s) 2: 3-regular graphs 2.1: FOR...
1: EDGES OF THE BIPARTITE GRAPH Please select file(s) Select image(s) 2: 3-regular graphs 2.1: FOR WHAT N IS THERE A SIMPLE 3-REGULAR GRAPH WITH N VERTICES? Please select file(s) Select image(s) 2.2 Please select file(s) Select image(s) 2.3 Please select file(s) Select image(s) 3:2-regular and 3-regular graphs 3.1: EVERY TWO CONNECTED 2-REGULAR GRAPHS WITH THE SAME NUMBER OF VERTICES ARE ISOMORPHIC. Please select file(s) Select image(s) 3.2: TWO CONNECTED, SIMPLE, 3-REGULAR GRAPHS WITH 8 VERTICES. Please select file(s) Select...
Problem 12.29. A basic example of a simple graph with chromatic number n is the complete graph on...
Problem 12.29. A basic example of a simple graph with chromatic number n is the complete graph on n vertices, that is x(Kn) n. This implies that any graph with Kn as a subgraph must have chromatic number at least n. It's a common misconception to think that, conversely, graphs with high chromatic number must contain a large complete sub- graph. In this problem we exhibit a simple example countering this misconception, namely a graph with chromatic number four that...
Let n >k> 1 with n even and k odd. Make a k-regular graph G by putting n vertices in a circle and...
need help with a and b in this graph theory question
Let n >k> 1 with n even and k odd. Make a k-regular graph G by putting n vertices in a circle and connecting each vertex to the exact a) Show that for all u,v there are k internally disjoint u, v-paths (you (b) Use the previous part, even if you did not prove it, to show that the e vertex and the k 1 closest vertices on either...
Answer each question in the space provided below. 1. Draw a simple graph with 6 vertices...
Answer each question in the space provided below. 1. Draw a simple graph with 6 vertices and 10 edges that has an Euler circuit. Demonstrate the Euler circuit by listing in order the vertices on it. 2. For what pairs (m,n) does the complete bipartite graph, Km,n contain an Euler circuit? Justify your answer. (Hint: If you aren't sure, start by drawing several eramples) 3. For which values of n does the complete graph on n vertices, Kn, contain a...
G3: I can determine whether a graph has an Euler trail (or circuit), or a Hamiltonian...
G3: I can determine whether a graph has an Euler trail (or circuit), or a Hamiltonian path (or cycle), and I can clearly explain my reasoning. Answer each question in the space provided below. 1. Draw a simple graph with 7 vertices and 11 edges that has an Euler circuit. Demonstrate the Euler circuit by listing in order the vertices on it. 2. For what pairs (m, n) does the complete bipartite graph, Km,n contain a Hamiltonian cycle? Justify your...
(7) Let V = {ui, U2 . . . . Un} with n > 4. In...
(7) Let V = {ui, U2 . . . . Un} with n > 4. In this exercise we will compute the probability that in a random graph with vertex set V we have that v and v2 have an edge between them or have an edge to a common vertex (i.e, have a common neighbour) (If you are troubled by my use of the term random we choose a graph on n vertices uniformly at random from the set...
Help with Java Program Please Create a simple graph class. The graph class should have the...
Help with Java Program Please Create a simple graph class. The graph class should have the following items: an adjacency list or matrix to hold the graph data variables to hold the current size and max size of the graph default constructor create empty adjacency list/matrix max size = 10 overloaded constructor create empty adjacency list/matrix max size = int parameter isEmpty check if current size is zero createGraph read a formatted file and fill adjacency list/matrix The first line...
(a) Given a graph G = (V, E) and a number k (1 ≤ k ≤...
(a) Given a graph G = (V, E) and a number k (1 ≤ k ≤ n), the CLIQUE problem asks us whether there is a set of k vertices in G that are all connected to one another. That is, each vertex in the ”clique” is connected to the other k − 1 vertices in the clique; this set of vertices is referred to as a ”k-clique.” Show that this problem is in class NP (verifiable in polynomial time)...
3 2 1 0 1 5 6 2 3 Graph of S State the values of...
3 2 1 0 1 5 6 2 3 Graph of S State the values of x for which the derivative is zero
Graph theory
a) prove that there is a 3 regular graph if n is even and
n>=4
b)
thank you
Exercise 4. How many distinct graphs are there with vertex set {1,2,...,n}? How many distinct graphs are there with vertex set {1,2,...,n} and m edges? For these questions, what happens if "with vertex set {1,2,...,n}" is replaced by "with n vertices"?
1: EDGES OF THE BIPARTITE GRAPH Please select file(s) Select image(s) 2: 3-regular graphs 2.1: FOR WHAT N IS THERE A SIMPLE 3-REGULAR GRAPH WITH N VERTICES? Please select file(s) Select image(s) 2.2 Please select file(s) Select image(s) 2.3 Please select file(s) Select image(s) 3:2-regular and 3-regular graphs 3.1: EVERY TWO CONNECTED 2-REGULAR GRAPHS WITH THE SAME NUMBER OF VERTICES ARE ISOMORPHIC. Please select file(s) Select image(s) 3.2: TWO CONNECTED, SIMPLE, 3-REGULAR GRAPHS WITH 8 VERTICES. Please select file(s) Select...
Problem 12.29. A basic example of a simple graph with chromatic number n is the complete graph on n vertices, that is x(Kn) n. This implies that any graph with Kn as a subgraph must have chromatic number at least n. It's a common misconception to think that, conversely, graphs with high chromatic number must contain a large complete sub- graph. In this problem we exhibit a simple example countering this misconception, namely a graph with chromatic number four that...
need help with a and b in this graph theory question
Let n >k> 1 with n even and k odd. Make a k-regular graph G by putting n vertices in a circle and connecting each vertex to the exact a) Show that for all u,v there are k internally disjoint u, v-paths (you (b) Use the previous part, even if you did not prove it, to show that the e vertex and the k 1 closest vertices on either...
Answer each question in the space provided below. 1. Draw a simple graph with 6 vertices and 10 edges that has an Euler circuit. Demonstrate the Euler circuit by listing in order the vertices on it. 2. For what pairs (m,n) does the complete bipartite graph, Km,n contain an Euler circuit? Justify your answer. (Hint: If you aren't sure, start by drawing several eramples) 3. For which values of n does the complete graph on n vertices, Kn, contain a...
G3: I can determine whether a graph has an Euler trail (or circuit), or a Hamiltonian path (or cycle), and I can clearly explain my reasoning. Answer each question in the space provided below. 1. Draw a simple graph with 7 vertices and 11 edges that has an Euler circuit. Demonstrate the Euler circuit by listing in order the vertices on it. 2. For what pairs (m, n) does the complete bipartite graph, Km,n contain a Hamiltonian cycle? Justify your...
(7) Let V = {ui, U2 . . . . Un} with n > 4. In this exercise we will compute the probability that in a random graph with vertex set V we have that v and v2 have an edge between them or have an edge to a common vertex (i.e, have a common neighbour) (If you are troubled by my use of the term random we choose a graph on n vertices uniformly at random from the set...
3 2 1 0 1 5 6 2 3 Graph of S State the values of x for which the derivative is zero
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