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Graphs (15 points) 14. For the following graph (8 points): a. Find all the edges that...
Consider the following graph. V(G) = {v1, v2, v3, v4}, e(G) = {e1, e2, e3, e4,...
Consider the following graph. V(G) = {v1, v2, v3, v4}, e(G) = {e1, e2, e3, e4, e5}, E(G) = {(e1,[v1,v2]),(e2,[v2,v3]),(e3,[v3,v4]), (e4, (v4,v1)), (e5,[v1,v3])} Draw a picture of the graph on scratch paper to help you answer the following two questions. How many edges are in a spanning tree for graph G? What is the weight of a minimum-weight spanning tree for the graph G if the weight of an edge is defined to be W (ei) L]?
suppose that we have a sample space s={E1,E2,E3,E4,E5,E6,E7}, where E1 to E7 denote the sample points....
suppose that we have a sample space s={E1,E2,E3,E4,E5,E6,E7}, where E1 to E7 denote the sample points. The following probability assignments apply: p(E1 )=.05 p(E2)=.20 P(E3)=.20 p(E4)=.25 p(E5)=.15 p(E6)=.10 and p(E7)=.05 Let A={E1,E4,E6} B={E2,E4,E7} C= {E2,E3,E5,E7} 1) Find A ∩ B and P(A ∩ B) and Are events A and C mutually exclusive?
3. Find the number of vertices and edges for the line graph L(G) of a graph...
3. Find the number of vertices and edges for the line graph L(G) of a graph G with the degree sequence (di, d2, , dp). (Note that all edges in G incident to the same vertex are pairwise adjacent in L(G).)
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more tha...
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more than one edge between the same pair of vertices) or self-loops (edges with both ends at the same vertex). [10 points] a. A graph with 3 connected components, 11 vertices, and 10 edges. b. A graph with 4 connected components, 10 vertices, and 30 edges. c....
Please answer question 2. Introduction to Trees Thank you 1. Graphs (11 points) (1) (3 points)...
Please answer question 2. Introduction to Trees
Thank you
1. Graphs (11 points) (1) (3 points) How many strongly connected components are in the three graphs below? List the vertices associated with each one. 00 (2) (4 points) For the graph G5: (a) (0.5 points) Specify the set of vertices V. (b) (0.5 points) Specify the set of edges E. (c) (1 point) Give the degree for each vertex. (d) (1 point) Give the adjacency matrix representation for this graph....
QUESTION 16 Consider the following graph and determine all edges that are adjacent to es. 42...
QUESTION 16 Consider the following graph and determine all edges that are adjacent to es. 42 UE U2 26 07 Us •14 ez, e4, es, and es e, and e ez, ez, e4, and e6 en, ez, e4, es, e6, and en
Can you please solve this fully Question 9 (10 marks) (i) How many vertices and how many edges do each of the following graphs have? [3 marks] (b) C16 (a) K70 (d) K2,5 (ii Suppose you have a graph G w...
Can you please solve this
fully
Question 9 (10 marks) (i) How many vertices and how many edges do each of the following graphs have? [3 marks] (b) C16 (a) K70 (d) K2,5 (ii Suppose you have a graph G with vertices vi, v. vi7. Explain (clearly) how you would use the adjacency matrix A to find a. The number of paths from v to vir of length 12.12 marks] b. The length of a shortest path from vi to...
8. For each of the following, either draw a undirected graph satisfying the given criteria or...
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more than one edge between the same pair of vertices) or self-loops (edges with both ends at the same vertex). [10 points] a. A graph with 3 connected components, 11 vertices, and 10 edges. b. A graph with 4 connected components, 10 vertices, and 30 edges. c....
4. (10 points) (a) An undirected graph has 6 vertices and 13 edges. It is known...
4. (10 points) (a) An undirected graph has 6 vertices and 13 edges. It is known three vertices have degree 3, one has degree 4, and another one has degree 7. Find the degree of the remaining vertex. (b) For each of the following graphs, determine if it is bipartite, complete, and/or a tree. Give a brief written or graphical justification for your answers (you may address multiple graphs at the same time). iii.
1. In the following graph, suppose that the vertices A, B, C, D, E, and F represent towns, and th...
question 1 and 2 please, thank
you.
1. In the following graph, suppose that the vertices A, B, C, D, E, and F represent towns, and the edges between those vertices represent roads. And suppose that you want to start traveling from town A, pass through each town exactly once, and then end at town F. List all the different paths that you could take Hin: For instance, one of the paths is A, B, C, E, D, F. (These...
Consider the following graph. V(G) = {v1, v2, v3, v4}, e(G) = {e1, e2, e3, e4, e5}, E(G) = {(e1,[v1,v2]),(e2,[v2,v3]),(e3,[v3,v4]), (e4, (v4,v1)), (e5,[v1,v3])} Draw a picture of the graph on scratch paper to help you answer the following two questions. How many edges are in a spanning tree for graph G? What is the weight of a minimum-weight spanning tree for the graph G if the weight of an edge is defined to be W (ei) L]?
3. Find the number of vertices and edges for the line graph L(G) of a graph G with the degree sequence (di, d2, , dp). (Note that all edges in G incident to the same vertex are pairwise adjacent in L(G).)
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more than one edge between the same pair of vertices) or self-loops (edges with both ends at the same vertex). [10 points] a. A graph with 3 connected components, 11 vertices, and 10 edges. b. A graph with 4 connected components, 10 vertices, and 30 edges. c....
Please answer question 2. Introduction to Trees
Thank you
1. Graphs (11 points) (1) (3 points) How many strongly connected components are in the three graphs below? List the vertices associated with each one. 00 (2) (4 points) For the graph G5: (a) (0.5 points) Specify the set of vertices V. (b) (0.5 points) Specify the set of edges E. (c) (1 point) Give the degree for each vertex. (d) (1 point) Give the adjacency matrix representation for this graph....
QUESTION 16 Consider the following graph and determine all edges that are adjacent to es. 42 UE U2 26 07 Us •14 ez, e4, es, and es e, and e ez, ez, e4, and e6 en, ez, e4, es, e6, and en
Can you please solve this
fully
Question 9 (10 marks) (i) How many vertices and how many edges do each of the following graphs have? [3 marks] (b) C16 (a) K70 (d) K2,5 (ii Suppose you have a graph G with vertices vi, v. vi7. Explain (clearly) how you would use the adjacency matrix A to find a. The number of paths from v to vir of length 12.12 marks] b. The length of a shortest path from vi to...
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more than one edge between the same pair of vertices) or self-loops (edges with both ends at the same vertex). [10 points] a. A graph with 3 connected components, 11 vertices, and 10 edges. b. A graph with 4 connected components, 10 vertices, and 30 edges. c....
4. (10 points) (a) An undirected graph has 6 vertices and 13 edges. It is known three vertices have degree 3, one has degree 4, and another one has degree 7. Find the degree of the remaining vertex. (b) For each of the following graphs, determine if it is bipartite, complete, and/or a tree. Give a brief written or graphical justification for your answers (you may address multiple graphs at the same time). iii.
question 1 and 2 please, thank
you.
1. In the following graph, suppose that the vertices A, B, C, D, E, and F represent towns, and the edges between those vertices represent roads. And suppose that you want to start traveling from town A, pass through each town exactly once, and then end at town F. List all the different paths that you could take Hin: For instance, one of the paths is A, B, C, E, D, F. (These...
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