1. True or False? Support your answer. (a) There is a graph with degree sequence 1,1,1,1....
2. For each of the following, draw a (simple) graph with the corresponding degree sequence, or explain why no such graph exists. (a) A graph with degree sequence 1, 1, 1, 1. (b) A graph with degree sequence 3, 3, 2, 2, 1, 1, 1. (c) A graph with degree sequence 4, 4, 4, 4, 4, 4. (d) A graph with degree sequence 6, 5, 4, 3, 2, 1
Can the sequence 6, 5, 4, 3, 2, 1 be the degree sequence of a simple graph? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a Yes b No Can the sequence 2, 2, 2, 2, 2, 2 be the degree sequence of a simple graph? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a Yes Selv b No Can the sequence...
Question 3 A graph has degree sequence 8,6,5,5,4,4,3,3. How many edges does it have? Input your answer as a single number. Selected Answer: [None Given]
Choose the true statement. There exists a graph with 7 vertices of degree 1, 2, 2, 3, 4, 4 and 5, respectively. the four other possible answers are false There exists a bipartite graph with 14 vertices and 13 edges. There exists a planar and connected graph with 5 vertices, 6 edges and 4 faces. There exists a graph with 5 vertices of degree 2, 3, 4, 5 and 6, respectively.
The degree sequence of the simple graph G is 17, 7, 5, 4, 4, 2, 2,1 (a) How many edges does G have? (Briefly explain your answer.) (b) What is the degree sequence of G (Briefly explain your answer.)
Give an example of a graph with two components that has degree sequence (1, 1, 1, 1, 1, 3, 3, 3). Discrete MathematicS
7. Give an example or prove that there are none: (a)A simple graph with degree sequence 1,2,2,3. (b)A simple graph with degree sequence 2,4,4,4,5.
Indicate whether you think the following statements are true, false or uncertain. Support your answer by giving all necessary reasoning and calculations: b) According to the quantity theory of money, “inflation is always and everywhere a monetary phenomenon.”
Are the following statements True / False / Uncertain? Support your answer with explanation. 1. It is even better for a perfectly competitive firm to produce output even though it is loosing money. 2. If the output elasticity of the total cost is less than one, we have disec- onomies of scale. 3. Inputs are perfect substitutes when one input can always be substitutes for the other on fixed terms and thus corresponding production function is called fixed-proportion production function....
Answer the following true or false questions with a brief justification. A) There exists an undirected graph on 6 vertices whose degrees are 4, 5, 8, 9, 3, 6. B) Every undirected graph with n vertices and n − 1 edges is a tree. C) Let G be an undirected graph. Suppose u and v are the only vertices of odd degree in G. Then G contains a u-v path.