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.) b a (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.

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.) b a (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.

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

(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.

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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.
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