Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Either find an Euler circuit in the following graph or explain why no such circuit exists.
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- For each 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 edge between two vertices with odd degree, find an Euler circuit in the resulting graph, and then delete the added edge from the circuit.) Figure 12: 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 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. Undirected edges, line segments, are between the following vertices: a and b; a and c; a and d; a and f; b and f; b and c; b and e; c and d; d and e; and d and f. Edges c f, a d, and b e intersect at the same point.arrow_forwardConsider the following portion of the London Tube (Underground) map as a graph with stops as vertices and the connecting lines (colored) as edges. Which of the following walks (listed as a sequence of tube stops) is not a cycle? Group of answer choices Charing Cross, Picadilly Circus, Green Park, Oxford Circus, Picadilly Circus, Charing Cross Charing Cross, Leicester Square, Tottenham Court Road, Oxford Circus, Picadilly Circus, Charing Cross Oxford Circus, Tottenham Court Road, Leicester Square, Picadilly Circus, Oxford Circus Picadilly Circus, Green Park, Oxford Circus, Tottenham Court Road, Leicester Square, Picadilly Circusarrow_forwardDoes the following graph contain an Euler circuit? Explain why or why not.arrow_forward
- 13. Consider the following graph: B F E Does it have an Euler circuit, an Euler path, or neither? Explain why.arrow_forwardDetermine an Euler circuit that begins with an vertex C in this Graph. arrow_forwardExplain 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.arrow_forward
- Is it possible for a graph to have both a Euler path and Euler circuit? Explain your answer.arrow_forwardIn 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.…arrow_forwardThe 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 Earrow_forward
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