Which of the following graphs have hamiltonian circuits? V S H Y Y O A В N S U R P V R |D

Q: Which of the following is a loop? * A E D BF CC BC O c

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Q: Given the adjacency matrix of an undirected graph abc a 213 b111 C 310 How many paths of length 3…

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Q: Which of the following graphs is Eulerian? 1. = II. A D A D [T] E B C [T] E B C F

A: Solution  :

Q: 5. Find the number of connected components in the following graphs. (a) V(G) = Z. Edges: m and n are…

A: Connected Components of a Graph : Connected components of a graph is a subgraph where there exist a…

Q: Which graphs have an Euler circuit? b а b a d f G H Select one: O a. Both G and H O b. Gonly Ос.…

A: Definition : Euler circuit An Euler circuit is a circuit that uses every edge in a graph with no…

Q: Find a Hamiltonian circuit inCay({(a, 0), (b, 0), (e, 1)}:Q4 ⨁ Z3).

A: Given:

Q: B H E RE OF G 3 A E D 2. Determine if each of the graphs above have a Hamiltonian circuit. Explain.

A: Remark: A path begins and ends on the same vertex (i.e., a closed circuit) such that each vertex is…

Q: Which of the following is NOTa circuit in the graph? * A B C F E D CC O ABFEA BFDCB O None of the…

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Q: (2) For the graph below (a) Find an Eulerian circuit, or prove that none exists. (b) Find a…

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Q: F A D E.

A: Given a graph G with vertices A, B, C, D, E, F, G. To find the Euler Path and Euler Circuit. Euler…

Q: Given the following graph; Which of the following is TRUE about the graph? O a. It is isomorphic to…

A: Solution: The graph is

Q: For a given graph G having n vertices and e edges which is connected and has no cycles, which of the…

A: In the question it is provided that a graph G with n vertices and e edges is connected and has no…

Q: hich of the following graphs have Euler circuits? H G N O A: Has Euler circuit. B: Has Euler…

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Q: 5. Find the number of connected components in the following graphs. (a) V(G) = Z. Edges: m and n are…

A: Given Data: (a) V(G)=Z  |mn|= 5  (b) V(G)=Z  |m-n|= 15 or |m-n|= 6 (c) V(G)=ZxZ  (|a-c|= 4…

Q: What is the Hamiltonian circuit in the given graph below? B E F D А. E -B-C-D- A-F-E В. A…

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Q: Which of the following graphs have hamiltonian circuits? F N DR H I O A OB R R OC |D

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Q: What is a circuit in the Hamiltonian and what edge can you remove to make a Hamilton path? K1 a (a,…

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Q: Find the number of paths of length 2 from a to c in the directed graph give a b d a 3 b|1 2 2 1 c| 2…

A: Given that,  The matrix representing the directed graph is    abc  dabcd0230122121101002

Q: Consider the tree diagram. Path number 0.4 D 1 0.6 2 0.5 D 3 4 A2. 0.5 D 4 2 0.7 D A3 0.3 D…

A: The tree diagram is given.

Q: If a graph G has a subgraph H with 1. |V(H)| = |V(G)I 2. H is connected 3. Je(H)| = |V(H)| 4. Vu E V…

A: A Hamiltonian cycle, Hamiltonian circuit, vertex tour or graph cycle is a cycle that visits each…

Q: If a graph G has a subgraph H with 1. ĮV(H)| = |V(G)| 2. H is connected 3. Je(H)| = |V(H)| %3D 4. Vu…

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Q: A В 7 1 4 5. 6 D 1 8 3 2 F E 2)

A: Since you have asked multiple questions, we'll solve the first question for you. If you want any…

Q: C D A E F Find any Hamiltonian circuit on the graph above. Give your answer as a list of vertices,…

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Q: Which of the following Hamiltonian circuits is obtained using greedy algorithrm? A 6. E 9. 3 10 1. 4…

A: A Hamiltonian path is a path that starts at any vertex of the graph and visits every vertex of the…

Q: Which of the following graphs have hamiltonian circuits? R VA OB I R K L OC OD

A: We will use definition of Hamiltonian circuit to answer the given question. A 'Hamiltonian circuit'…

Q: Which of the following four graphs on five vertices is not isomorphic to any of the other three?…

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Q: Using the following graph, find an Euler circuit that begins and ends with vertex C. FO В…

A: An euler circuit in a graph is a circuit that uses every edge of the graph exactly once

Q: What is the Hamiltonian circuit in the given graph below? B. F D. B- F C- E - D - A – B А - D - E -…

A: For the Hamiltonian circuit, the vertex of the graph is visited exactly once. Since, it is a…

Q: Suppose G has V vertices and E edges. Let M and m denote, respectively, the maximum and minimum of…

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Q: B. Graph the preimage of MNPO across the line of reflection y-4 -2(x+ 3) M' N' O' P'

A: Since you have posted multiple questions, we will solve only first question for you. To get…

Q: 3) What is the adjacency matrix Ac for the following graph G based on the order of the vertices a,…

A: Note: Since you have asked multiple independent questions, we are only allowed to answer one. Thank…

Q: Theorem. For every m E N and graph G = (V, E), if: %3D • Every vertex v E V has d(v) > m then: •…

A: We prove the given statement by induction on m. Assume that m=1. Given that every vertex v has dv≥1.…

Q: Which of the following is a loop? F C E D BF CC BC C

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Q: Which of the following is NOT a circuit 1 point in the graph? * A F E CC ABFEA BFDCB O None of the…

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Q: 1. Which of the following is NOT a circuit in the graph? E FO OA) CBEC OB) ABEA 0 C) BCDCB Figure 1…

A: Vertex is where two or more edges meet. The circuit is a path in a connected graph in which the…

Q: Which of the following is a loop? * A B F E D BF О сс О вс C

A: Note: We know that in graph theory, a loop is an edge that starts and ends with the same vertex.…

Q: Which of the following is TRUE about the graph? O a. It is isomorphic to K5 O b. It has a…

A: To find the correct option

Q: Consider the tree diagram. Path number 0.4 D 1 A1 0.6 2 0.5 D 3 A2. 0.5 D 0.7 D 5 A3 0.3 D Which…

A: =     P(A1∩ )/P(A1)

Q: a e d b C

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Q: Which of the following graphs G = ({1,2, 3, 4, 5}, {a, b, c, d, e, f}) have an Euler circuit? Select…

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Q: a. Let V = (x, y, z, u, v). How many distinct graphs are there on the exactly 6 edges? (Note that…

A: (a) The set of vertices given is as follows: V=x, y, z, u, v We know that the total sum of degrees…

Q: Which one of the following statements is NOT true about this graph? A B F C E O There is a circuit…

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Q: 03. Which of the following graphs has a positive region of (-0, -4). A. в. C. D. E. not given

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Q: A B E D

A: Remark: A path of a graph that passes through every vertex of the graph exactly once and returns to…

Q: If a graph G has a subgraph H with 1. [V(H)| = |V(G)| 2. H is connected 3. Je(H)| = |V(H)| %3D 4. Vu…

A: The necessary condition for a graph to be Hamiltonian circuit is that the graph must be connected,…

Q: Determine if the graph is i) Eulerian only, then specify an Eulerian circuit ii) Hamiltonian only,…

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Q: Identify the folllowing:  a. V(G) b. p  c. E(G) d. Shortest path from b to g

A: # It is not clear what p denotes in (b)   (a) The number of vertices V(G) in the graph is 7. The…

Q: is a cycle (closed walk) of length 2. O True O False

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Q: a. Let V = {x, y, z, u, v}. How many distinct graphs are there on the vertex set V with exactly 6…

A: We have given graph V{x,y,w,u,z} We need to calculate a)graph having 6 edges. b) The trail which is…