7. Give an example or prove that there are none: (a)A simple graph with degree sequence...
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
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
Prove that in every simple graph there is a path from every vertex of odd degree to a vertex of odd degree.
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...
a) Let G be a simple graph with degree sequence (6,6,4,4,4, 2,2). Can you guarantee that G has an Euler path? Justify your answer. b) Determine the chromatic number of the graph shown below vi V2 VS V3 VA
1. True or False? Support your answer. (a) There is a graph with degree sequence 1,1,1,1. (b) There is a graph with degree sequence 3, 3,3, 3. (c) There is a graph with degree sequence 3,2,1,1.
topic: graph theory Question 5. Prove that every graph with at least two vertices contains two vertices with the same degree. Then for each n 2 2 give an example of a graph with n vertices which does not have three vertices of the same degree. Question 5. Prove that every graph with at least two vertices contains two vertices with the same degree. Then for each n 2 2 give an example of a graph with n vertices which...
Let G be a simple graph with at least four vertices. a) Give an example to show that G can contain a closed Eulerian trail, but not a Hamiltonian cycle. b) Give an example to show that G can contain a closed Hamiltonian cycle, but not a Eulerian trail.
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...