Analyze each graph and explain why the graph does or does not have an Euler circuit. If it does, specify the nodes within the circuit. b e a (i) Figure 6: 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 verter becomes the rightmost verter. From the bottom left verter, moving clockwise, the vertices in the pentagon shape are labeled: a, b, c, e, and f. Verter d is above verter e, below and to the right of verter c. Undi- rected 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.

Analyze each graph and explain why the graph does or does not have an Euler circuit. If it does, specify the nodes within the circuit. b e a (i) Figure 6: 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 verter becomes the rightmost verter. From the bottom left verter, moving clockwise, the vertices in the pentagon shape are labeled: a, b, c, e, and f. Verter d is above verter e, below and to the right of verter c. Undi- rected 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.

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

Analyze each graph and explain why the graph does or does not have an Euler circuit. If it does,
specify the nodes within the circuit.
b
e
a
(i)
Figure 6: 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 verter becomes the rightmost
verter. From the bottom left verter, moving clockwise, the vertices in the pentagon shape are
labeled: a, b, c, e, and f. Verter d is above verter e, below and to the right of verter c. Undi-
rected 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.

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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.
Plz answer both the question in 20 minutes
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.
For each graph below, find an Euler circuit in the graph or explain why the graph does not have an Euler circuit. (a) 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. IHence, the top verter becomes the rightmost verter. From the bottom left verter, moving clockwise, the vertices in the pentagon shape are labeled: a, b, c, e, and f. Verter d is above verter e, below and to the right of vertex c. Undirected edges, line segments, are between the following vertices: b and e; b and a; b and f; b and e; a and e; a and d; a and f; e and d; e and f; d and e; and d and f. (b) g 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. Ilence, the top verter becomes the rightmost verter. From the bottom left verter, moving clockwise, the vertices and f. Verter d is above vertex e, below and to the right of verter e. Verter g…
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.
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.
For the graph below, find an Euler trail in the graph or explain why thegraph does not have an Euler trail.
Tessa wants to deliver the mail. She begins at the Post Office where she picks up the mail each day, but wants to end close to her home. She only wants to go down each street once. Her home is 5 miles from the Post Office. Which graph would best meet this scenario? a.) Hamiltonian path b.) Hamiltonian cycle c.) Euler tour d.) Euler path