55. Explain why the graph shown to the right has no Euler pathsand no Euler circuits.BThis graph has 4oddIver tices.SoithasHho Eulerpath F Euler Carcuit,.Choose the correct answer below.A. By Euler's Theorem, the graph has no Euler paths and no Euler circuits because it has an even numberof odd vertices.B. By Euler's Theorem, the graph has no Euler paths and no Euler circuits because it has exactly two oddvertices.C. By Euler's Theorem, the graph has no Euler paths and no Euler circuits because it has morethan two odd vertices.D. By Euler's Theorem, the graph has no Euler paths and no Euler circuits because it has all evenvertices. In question # 55, why the how many odd vertices do thegiven vertices have? Does this graph have Euler Path, EulerCircuit, or Neither?

Answered: Image /qna-images/answer/7517c3b0-dbc1-44ef-801f-8bc78a7ce749.jpg

Answered: 55. Explain why the graph shown to the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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12. If G is a simple graph with vertices a, b, c, d, e and d(a) = d(b) = d(c) = 3 (d = degree), then the maximum possible number of edges of G is O 7 9. 8.
Explain why the graph shown to the right has no Euler paths and no Euler circuits. A B D. E G H. ..... Choose the correct answer below. O A. By Euler's Theorem, the graph has no Euler paths and no Euler circuits because it has all even vertices. O B. By Euler's Theorem, the graph has no Euler paths and no Euler circuits because it has exactly two odd vertices. O C. By Euler's Theorem, the graph has no Euler paths and no Euler circuits because it has more than two odd vertices. O D. By Euler's Theorem, the graph has no Euler paths and no Euler circuits because it has an even number of odd vertices.
36. What is the size of the special graph Kmn? A. m+n B. 2(m+n) C. mn D. 2(n-1) 36
Kindly solve both parts correctly and handwritten
1. For each graph below determine whether or not they contain an Eulerian circuit, an Eulerian trail, or neither. Justify your answers (you do not need to find the circuits or trails). >0 Show Transcribed Text (a) For each graph below determine whether or not they contain an Eulerian circuit, an Eulerian trail, or neither. Justify your answers (you do not need to find the circuits or trails).
(c) For cach graph below, find an Euler trail in the graph or explain why the graph does not have an Euler trail. (Hint: One way to find an Euler trail is to add an cdge between two vertices with odd degree, find an Euler circuit in the resulting graph, and then delete the added edge from the circuit.) (i) Figure 11: An undirected graph has 6 vertices, a through f. 5 vertices are in the form of a regular pentagon, rotated 90 degrees clockwise. Hence, the top vertez becomes the rightmost vertez. From the bottom left vertez, moving clockwise, the vertices in the pentagon shape are labeled: a, b, c, e, and f. Vertez d is above vertez e, below and to the right of vertez c. Undirected edges, line segments, are between the following vertices: a and b; a and e; a and d; a and f; b and f; b and e; e and d; e and f; d and e; and d and f.
71. Answer the following questions for graph G below, which was created to represent the roads of a shopping mall. C B A (a) Determine the number of vertices and edges of the graph. (b) Determine the valences of the vertices A, F, and D. (c) If the graph has an Euler circuit, write it down starting with vertex E.
A school bus wants to take fifteen students from their houses in a particular area. In the following graph, the houses are represented by vertices, while the streets connecting the houses are represented by edges. 7.a: Determine if there is a path that the school bus can take to reach all students, such that it does not cross the same house more than one time, and find if it can also do so while return back to the starting house. 7.b: Determine if there is a path that the school bus can take to reach all students, such that it does not cross the same street more than one time, and find if it can also do so while return back to the starting house.
17. Given the following degree of the vertices of an undirected graph H= {4,1,5,3,4,3}, we can conclude that: A. Graph H is a graph and there is an end vertex in graph H B. Graph H is a graph and there is an isolated vertex in graph H C. Graph H is not a graph D. We cannot conclude anything. 17
B Complete the following for the graph on the right. a. Determine if the graph must have Hamilton circuits. G b. If the graph must have Hamilton circuits, determine the number of such H circuits. K ..... a. Must the graph have Hamilton circuits? O A. Yes, it must because it is complete and has at least three vertices. O B. Yes, it must because it is not complete. O C. No, it might not because it is complete and has at least three vertices. OD. No, it might not because it is not complete. b. How many circuits, if any, does the graph have? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The graph has Hamilton circuits. O B. The graph does not have any Hamilton circuits.

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