b)Figure 3Referring to Figure 3, determine whether the given graph has an Euler circuit. Write downsuch a circuit when one exists. If no Euler circuit exists, determine whether the graph hasan Euler path and write down such a path if one exists.

An Euler path is a path that starts at any vertex of the graph and traverses each edge of the graph…

Answered: Figure 3 Referring to Figure 3,…

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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13. Consider the following graph: B F E Does it have an Euler circuit, an Euler path, or neither? Explain why.
Please solve the right side which is the shape as a rectangle
Which of the following graphs have hamiltonian circuits? DA OB
Choose the correct statement. O An Euler circuit for a given graph G contains every vertex at least once and every edge at least once. O An Euler circuit for a given graph G contains every vertex exactly once and not necessarily contain all edges of G. O An Euler circuit for a given graph G contains every vertex at least once and every edge exactly once. O An Euler circuit for a given graph G contains every vertex exactly once and every edge exactly once. Next page EN
Explain why the graph does or does not have an Euler circuit. If it does, specify the nodes within the circuit Figure 9: An undirected graph has 7 vertices, a through g. 5 vertices are in the form of a regular pentagon, rotated 90 degrees clockwise. Hence, the top vertex becomes the rightmost vertex. From the bottom left vertex, moving clockwise, the vertices in the pentagon shape are labeled: a, b, c, e, and f. Vertex d is above vertex e, below and to the right of vertex c. Vertex g is below vertex e, above and to the right of vertex f. Undirected edges, line segments, are between the following vertices: a and b; a and c; a and f; b and f; b and c; c and d; c and g; d and e; d and f; and f and g.
The following graph contains an Euler path. a b a) (3 points) What is the necessary and sufficient condition a graph must have in order to have an Euler path b) (3 points) List one Euler path from the graph.
Is it possible for a graph to have both a Euler path and Euler circuit? Explain your answer.
The shown figures are the Euler circuit. Identify their paths and enumerate their vertices.
In your own words, explain what is required for a trail or circuit to be a Euler trail or circuit. Does a Euler trail exist for their graph? Explain specifically using the label and degree of each vertex. Does a Euler circuit exist for their graph? Explain specifically using the label and degree of each vertex. There are 6 people that discussing their favorite foods. Each person will be represented with a letter. A, B, C, D, E, F. Person A, B, and C really like Ice cream. Person D really likes cookies. Person A and C agree that cookies are good. Person D, C, and E like soup quite a bit, and person C, B, and E really like salad. Person B, E, and F all agree that cake is good too. So, person A really likes ice cream and cookies. Person B really likes ice cream, salad, and cake. Person C really likes ice cream, cookies, soup, and salad. Person D really likes cookies and soup. Person E really likes salad and cake. Person F only likes cake. The below graph represents this relationship.…
The graph shown has at least one Euler circuit. Determine an Euler circuit that begins and ends with vertex C. Complete the path so that it is an Euler circuit. C, A, B, E, D, A, 0 ... (.... D B E
6. Determine whether the given graph has an Euler circuit. Construct such a circuit when one exists. If no Euler circuit exists, determine whether the graph has an Euler path and construct such a path if one exists. Write the reason your answer is correct. Euler Circuit: Yes No Euler Path: Yes No b Ø d a Reason: Reason: Euler Path/Circuit:

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Figure 3 Referring to Figure 3, determine whether the given graph has an Euler circuit. Write down such a circuit when one exists. If no Euler circuit exists, determine whether the graph has an Euler path and write down such a path if one exists.