Find the euler circuit from the following graph ba1. O g, f, h, e, d, с, b, a, g.2. О а, b, с, d, е, с, һ, b, f, h, е, f, g, a.3. О а, b, с, d, e, h, f, g, а.4. O d, с, е, h, f, b, a, g, f, e, d.

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Answered: b a 1. O g, f, h, e, d, с, b, a, g. 2.…

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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For each graph below, ﬁnd an Euler circuit in the graph or explain why the graph does not have an Euler circuit. Figure 9: 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: b and c; b and a; b and f; b and e; a and c; a and d; a and f; c and d; c and f; d and e; and d and f.
Determine whether the following graph is strongly connected
Identify if the following graphs have an Euler Circuit or NOT. Fill in the space provided for each picture with EULERIAN if it has an Euler Graph and NOT EULERIAN if it does not have one. → → 1. A 2 B A B B O EQ
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.
Consider the graph H below. (a) Does H have an Euler circuit? If one exists, explain why, and then label the starting vertex and number the edges in the order in which they are traversed. If not, explain why one doesn't exist. 9.
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.
I'm trying to figure out which of the graphs as an Euler Path, and why?
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.
10. For each of the following, draw the graph or explain why the graph cannot exist: (c) A complete graph which does not have an Euler Circuit. (d) A simple graph with degrees 0,1,1,2,2,3,3,4,5.
(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.
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b a 1. O g, f, h, e, d, с, b, a, g. 2. О а, b, с, d, е, с, һ, b, f, h, е, f, g, a. 3. О а, b, с, d, e, h, f, g, а. 4. O d, с, е, h, f, b, a, g, f, e, d.