What is the total degree of a graph?
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(a) What is the degree of each vertex in the K7 graph shown below? (b) Does the graph possess and Euler Circuit, and Euler Path, or neither? (c) Find the number of edges in the graph.
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...
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
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
For a directed graph the in-degree of a vertex is the number of edges it has coming in to it, and the out- degree is the number of edges it has coming out. (a) Let G[i,j] be the adjacency matrix representation of a directed graph, write pseudocode (in the same detail as the text book) to compute the in-degree and out-degree of every vertex in the Page 1 of 2 CSC 375 Homework 3 Spring 2020 directed graph. Store results...
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.
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.
The graph to the right is a graph of a polynomial function. 10 (A) What is the minimum degree of a polynomial function that could have the graph? B (B) Is the leading coefficient of the polynomial function negative or positive? -10 (A) What is the minimum degree of a polynomial function that could have the graph? (Type a whole number.)
An odd graph is one where each vertex is of odd degree. Show that a graph is odd if and only if a(X) = |x|(mod2) for each subset X of V.
3. Identify (circle) the degree and leading coefficient for each graph. Degree (1/2 Pt): Degree (1/2 Pt): Degree (1/2 Pt) Degree (1/2 Pt): Odd Even Odd v Odd Even Odd Even Leading Coefficient (1/2 Pt): Leading Coefficient (1/2 t): Leading Coefficient (1/2 Pt): Leading Coefficient (1/2 Pt): PositiveNegative Positiveegative PositiveNegative Positive Negative 6 pts