N L Q Consider the graph given above. Add an edge so the resulting graph has an Euler circuit (without repeating an existing edge). Now give an Euler circuit through the graph with this new edge by listing the vertices in the order visited.

N L Q Consider the graph given above. Add an edge so the resulting graph has an Euler circuit (without repeating an existing edge). Now give an Euler circuit through the graph with this new edge by listing the vertices in the order visited.

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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QUESTION 20 Choose the true statement for the following graph. A B D E Oa. The graph has an Euler circuit. Ob. The graph has an Euler path. Oc. The graph has neither an Euler circuit nor an Euler path. Od. The graph has both an Euler circuit and an Euler path.
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.
Find a Hamilton circuit for each graph below. Hamilton circuit for Kut Hamilton circuit for Kz Hamilton circuit for Kg:
Find an Euler circuit for each graph below. b. Graphs K2 K1 K3 Euler circuit for K: • Euler circuit for K2: Euler circuit for K3:
For the following graph, explain, giving reason for your answer, why an Euler circuit exists. Indicate the circuit. a 8 e h j
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).
For each graph below, ﬁnd an Euler circuit in the graph or explain why the graph does not have an Euler circuit. Figure 10: 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 d; a and f; b and f; b and c; b and e; c and d; c and g; d and e; d and f; and f and g.
(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.
Does the following graph have an Eulerian circuit? An Eulerian path? If so give the circuit / path.