Give an example of a graph with two components that has degree sequence (1, 1, 1, 1, 1, 3, 3, 3). Discrete MathematicS
Give an example of a graph with two components that has degree sequence (1, 1, 1,...
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.
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.
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
Recall the definition of the degree of a vertex in a graph. a)
Suppose a graph has 7 vertices, each of degree 2 or 3. Is the graph
necessarily connected ?
b) Now the graph has 7 vertices, each degree 3 or 4. Is it
necessarily connected?
My professor gave an example in class. He said triangle and a
square are graph which are not connected yet each vertex has degree
2.
(Paul Zeitz, The Art and Craft of Problem...
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...
Give an example of a sequence (a) with (a0, but an divergent example of a sequence (an) with (an) 0, but Σ an divergent
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]
8 that has exactly two vertices of the- Provide an example of a graph G of order n same degree, or prove that no such graph exists.
A graph has 21 edges, two vertices of degree 5, four vertices of degree 3, and all remaining vertices have degree 2. How many vertices does the graph have? 12 10 16 O 14
5. Give an example of a bounded sequence {sn)1 such that the set con- sisting of all its subsequential limits is precisely the closed interval [0, 1]. (Prove that your example has this property).