Consider the graph below (a) How many edges are in this graph? (b) How many regions are in this graph? (c) Create a matrix called A in Matlab to be the adjacency matrix of this graph. (please upload the Matlab Code using the last question on the exam). Use Matlab to find the number of ways to travel from v2 to v3 in 5 steps = (d) True or False: S6 is a subgraph of the given graph (respond T or F) (e) True or False: S6 is a spanning tree of the given graph (respond T or F)
Added by Christina M.
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(a) There are 9 edges in this graph. Show more…
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In each question below, circle either TRUE (T) or FALSE (F). If a graph contains a cycle that includes all of the edges of the graph, then the cycle is an Euler Cycle. In any graph, the number of nodes of odd degree is even. If a graph has no cycles, then the graph is a tree. If a graph has one face, then the graph has no cycles. If a graph has more than one spanning tree, then the graph must have a cycle. (B) Suppose a graph is represented by an adjacency matrix A. Also, suppose the row and column entry of A is 9. What exactly does this mean? Be specific. Draw the complement of the following graph.
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QUESTION 1 A graph has vertex set V = {A, B, C, D, E, F} and edge set E = {{A, E}, {A, F}, {B, C}, {B, D}, {C, D}, {E, F}}. a. What is the order of this graph? b. How many components does this graph have? c. What is the degree (or valence) of vertex B? QUESTION 2 A graph has vertex set V = {A, B, C, D, E, F} and edge set E = {{A, E}, {A, F}, {B, C}, {B, D}, {C, D}, {E, F}}. This graph is connected. True False QUESTION 3 Consider the graph below. A → F → E → A is a simple circuit. True False QUESTION 4 Consider the graph below. B → C → D → B is an Euler circuit. True False QUESTION 5 Consider the graph below. B → C → D → E → F → A → D → B is a Hamilton circuit. True False
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Decide whether the following statements are true or false. (a) If G is a connected simple graph and e is an edge of G, then there is a spanning tree of G that contains e. (b) If G is a connected simple graph and e and f are edges of G, then there is a spanning tree of G that contains e and f. (c) If G is a connected simple graph and e, f and g are edges of G, then there is a spanning tree of G that contains e, f and g. (d) If G is a connected simple graph and F is a cycle-free set of edges in G, then there is a spanning tree of G that contains F.
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