QUESTION 21 Given the adjacency matrix of a graph: (0 20020) 0 1101 0 120 0 0 0 10 Answer the following questions. • What is the order of the graph? • How many parallel edges are there? • How many loops are there? • What is the sum of all degrees? For the following statement, type Tif it is true or F if it is false. · The graph has an Eulerian path.
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- 8. Answer the following questions for a random graph generated by the Erdos-Renyi random graph model ER(n, p). You do not need to prove your answers are correct but still need to show your work. Your answer should be in terms of n and p. 8(a) What is the expected number of triangles? 8(b) What is the probability that d(u, v) > 2 for two particular vertices u v? (Hint: First, find the probability that d(u, v) > 1. Then consider, for all other vertices x, the probability that uxv is NOT a path in the random graph. Multiply all these probabilities together.) Note that for this question, no graph is given. However, we know that the expected number of edges for ER(n, p) random graph model is , and that the expected degrees of the vertex for the random graph model ER(n, p) is (n-1) *pExercise 1 In each of the following questions V=[n]={1,2,...,n}. What is the number of (simple undirected) graphs G=(V,E) ? What is the number of (simple undirected) graphs G=(V,E) with no isolated vertices ? Prove your answers and show your work step by stepConsider the graph depicted below. Answer the following questions: What is the degree of vertex a? What is the sum of degrees of all vertices? Who are the neighbors of vertex f? [Please, give the list in alphabetical order, separating letters with only a comma. Do not insert blank spaces] How many zeros does the adjacency matrix of the graph above contain? What is the value on row g and column d of the adjacency matrix?
- 2 Letbe a graph with:(a) What is the largest number of edges that such a graph can have? "explain in details"(b) What is the smallest number of edges that such a graph can have? "explain in details"Give an example of an application of a graph in computer science.Indicate whether the graph is directed or undirected. What significance, if any, does the presence of cycles have in this graph?Also indicate what significance, if any, there is to whether the graph is connected. Please provide reference at the end also and dont copy from other sites . I need detailed answer with graph also. Someone has posted ans here it was not up to mark and not sufficient .An Euler path, in a graph or multigraph, is a walk through the graph which uses every edge exactly once. An Euler circuit is an Euler path which starts and stops at the same vertex. NOTE: graphs are in the image attached. Which of the graphs below have Euler paths? Which have Euler circuits? List the degrees of each vertex of the graphs above. Is there a connection between degrees and the existence of Euler paths and circuits? Is it possible for a graph with a degree 1 vertex to have an Euler circuit? If so, draw one. If not, explain why not. What about an Euler path? What if every vertex of the graph has degree 2. Is there an Euler path? An Euler circuit? Draw some graphs. Below is part of a graph. Even though you can only see some of the vertices, can you deduce whether the graph will have an Euler path or circuit? NOTE: graphs is in the image attached.
- Construct a directed network whose vertices represent the numbers 11, 12, 13, 15, 17 and whose weights tell how much you must add to get from one vertex to another. Include only edges of positive weight. include verbal descriptions/explanations, proofs, relevant tables and graphs, and clear labeling (of sections of the document and plots)1. What type of graph is represented? 2. List the vertices that are represented on the graph? 3. List the edges that are represented on the graph? 4. What is the cost or distance from Philadelphia to Detroit? 5. Give the weight of each edge that is traversed to get from Philadelphia to Detroit 6. What would be the longest path from Pittsburgh to Chicago? 7.Given a vertex set W = {1, 2, 3, 4}, solve for the following questions: (i) Knowing that edges are the same if and only if they have the same endpoint, how many different edges are possible? (ii) Suppose for this question that graphs are different if they have different sets of edges (they do not depend on if the graphs are isomorphic or not). How many simple graphs are there with the vertex set W? (iii) Draw the eleven nonisomorphic simple graphs that have four vertices.
- For the following graph, answer the questions. (a) Report the order of the vertices encountered on a breadth-first search starting from vertex A. Break all ties by picking the vertices in alphabetical order (i.e., A before Z). (b) Report the order of the vertices encountered on a depth-first search starting from vertex A. Break all ties by picking the vertices in alphabetical order (i.e., A before Z).Answer True or False to the following claims: a. If G is graph on at most 5 vertices and every vertex has degree 2, then G is a cycle. b. Let G be a forest. If we add an edge to G, then G is no longer a forest. c. Let G be a graph, and let u, v, and w be vertices in G. Suppose that a shortest path from u to v in G is of length 3, andsuppose that a shortest path from v to w in G is of length 4. Then a shortest path from u to w in G is of length 7.let a graph have vertices h,i,j,k,l,m,n,o and edge set {{h,i},{h,j},{h,k},{h,n},{h,o},{j,k},{j,l},{j,m},{k,l},{m,o},. on paper, draw the graph. then answer the questions below. a. what is the degree of vertex k? b. what is the degree of vertex h? c. how many connected components does the graph have?