Prove that the two graphs below are isomorphic. Figure 4: Two undirected graphs. Each graph has 6 vertices. The ver- tices in the first graph are arranged in two rous and 3 columns. From left to right, the vertices in the top row are 1, 2, and 3. From left to right, the vertices in the bottom row are 6, 5, and 4. Undirected edges, line segments, are between the following vertices: 1 and 2; 2 and 3; 1 and 5; 2 and 5; 5 and 3; 2 and 4; 3 and 6; 6 and 5; and 5 and 4. The vertices in the second graph are a through f. Vertices d, a, and c, are vertically inline. Vertices e, f, and b, are horizontally to the right of vertices d, a, and c, respectively. Undirected edges, line segments, are between the following vertices: a and d; a and c; a and e; a and b; d and b; a and f; e and f; c and f; and b and f. Show that the pair of graphs are not isomorphic by showing that there is a property that is preserved under isomorphism which one graph has and the other does not. Figure 5: Two undirected graphs. The first graph has 5 vertices, in the form of a regular pentagon. From the top verter, moving clockwise, the vertices are labeled: 1, 2, 3, 4, and 5. Undirected edges, line segments, are between the following vertices: 1 and 2; 2 and 3; 3 and 4; 4 and 5; and 5 and 1. The second graph has 4 vertices, a through d. Vertices d and c are horizontally inline, where verter d is to the left of verter c. Verter a is above and between vertices d and c. verter b is to the right and belouw verter a, but above the other two vertices. Undirected edges, line segments, are between the following vertices: a and b; b and c; a and d; d and c; d and b.
Prove that the two graphs below are isomorphic. Figure 4: Two undirected graphs. Each graph has 6 vertices. The ver- tices in the first graph are arranged in two rous and 3 columns. From left to right, the vertices in the top row are 1, 2, and 3. From left to right, the vertices in the bottom row are 6, 5, and 4. Undirected edges, line segments, are between the following vertices: 1 and 2; 2 and 3; 1 and 5; 2 and 5; 5 and 3; 2 and 4; 3 and 6; 6 and 5; and 5 and 4. The vertices in the second graph are a through f. Vertices d, a, and c, are vertically inline. Vertices e, f, and b, are horizontally to the right of vertices d, a, and c, respectively. Undirected edges, line segments, are between the following vertices: a and d; a and c; a and e; a and b; d and b; a and f; e and f; c and f; and b and f. Show that the pair of graphs are not isomorphic by showing that there is a property that is preserved under isomorphism which one graph has and the other does not. Figure 5: Two undirected graphs. The first graph has 5 vertices, in the form of a regular pentagon. From the top verter, moving clockwise, the vertices are labeled: 1, 2, 3, 4, and 5. Undirected edges, line segments, are between the following vertices: 1 and 2; 2 and 3; 3 and 4; 4 and 5; and 5 and 1. The second graph has 4 vertices, a through d. Vertices d and c are horizontally inline, where verter d is to the left of verter c. Verter a is above and between vertices d and c. verter b is to the right and belouw verter a, but above the other two vertices. Undirected edges, line segments, are between the following vertices: a and b; b and c; a and d; d and c; d and b.
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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Transcribed Image Text:Prove that the two graphs below are isomorphic.
Figure 4: Two undirected graphs. Each graph has 6 vertices. The ver-
tices in the first graph are arranged in two rous and 3 columns. From left
to right, the vertices in the top row are 1, 2, and 3. From left to right, the
vertices in the bottom row are 6, 5, and 4. Undirected edges, line segments,
are between the following vertices: 1 and 2; 2 and 3; 1 and 5; 2 and 5; 5
and 3; 2 and 4; 3 and 6; 6 and 5; and 5 and 4. The vertices in the second
graph are a through f. Vertices d, a, and c, are vertically inline. Vertices
e, f, and b, are horizontally to the right of vertices d, a, and c, respectively.
Undirected edges, line segments, are between the following vertices: a and
d; a and c; a and e; a and b; d and b; a and f; e and f; c and f; and b and
f.
Show that the pair of graphs are not isomorphic by showing that there
is a property that is preserved under isomorphism which one graph has and
the other does not.
Figure 5: Two undirected graphs. The first graph has 5 vertices, in the
form of a regular pentagon. From the top verter, moving clockwise, the
vertices are labeled: 1, 2, 3, 4, and 5. Undirected edges, line segments, are
between the following vertices: 1 and 2; 2 and 3; 3 and 4; 4 and 5; and
5 and 1. The second graph has 4 vertices, a through d. Vertices d and c
are horizontally inline, where verter d is to the left of verter c. Verter a
is above and between vertices d and c. verter b is to the right and belouw
verter a, but above the other two vertices. Undirected edges, line segments,
are between the following vertices: a and b; b and c; a and d; d and c; d
and b.
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