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This problem will use the concept of a graph's degree sequence. This is a list of the degrees of all the vertices in the graph, in descending order of degree. For example, the graph a has degree sequence (4,3, 3, 2, 2,0) because there is one node with degree 4 (c), two nodes with degree 3 (b and d), two nodes with degree 2 (a and e), and one node with degree 0 (f). For each of the following, either list the set of edges of a tree with vertex set {a, b, c, d, e, f} that has the stated degree sequence, or show that no such tree exists. (a) (3, 3, 3, 1, 1, 1) (b) (3,3, 1, 1, 1, 1) (c) (4,3, 1, 1, 1, 1)

This problem will use the concept of a graph's degree sequence. This is a list of the degrees of all the vertices in the graph, in descending order of degree. For example, the graph a has degree sequence (4,3, 3, 2, 2,0) because there is one node with degree 4 (c), two nodes with degree 3 (b and d), two nodes with degree 2 (a and e), and one node with degree 0 (f). For each of the following, either list the set of edges of a tree with vertex set {a, b, c, d, e, f} that has the stated degree sequence, or show that no such tree exists. (a) (3, 3, 3, 1, 1, 1) (b) (3,3, 1, 1, 1, 1) (c) (4,3, 1, 1, 1, 1)

Advanced Engineering Mathematics
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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This problem will use the concept of a graph's degree sequence. This is a list of the degrees of all the vertices in the graph, in descending order of degree. For example, the graph has degree sequence (4,3, 3, 2, 2,0) because there is one node with degree 4 (c), two nodes with degree 3 (b and d), two nodes with degree 2 (a and e), and one node with degree 0 (f). For each of the following, either list the set of edges of a tree with vertex set {a, b, c, d, e, f} that has the stated degree sequence, or show that no such tree exists. (a) (3,3, 3, 1, 1, 1) (b) (3, 3, 1, 1, 1, 1) (c) (4,3, 1, 1, 1, 1)
Transcribed Image Text:This problem will use the concept of a graph's degree sequence. This is a list of the degrees of all the vertices in the graph, in descending order of degree. For example, the graph has degree sequence (4,3, 3, 2, 2,0) because there is one node with degree 4 (c), two nodes with degree 3 (b and d), two nodes with degree 2 (a and e), and one node with degree 0 (f). For each of the following, either list the set of edges of a tree with vertex set {a, b, c, d, e, f} that has the stated degree sequence, or show that no such tree exists. (a) (3,3, 3, 1, 1, 1) (b) (3, 3, 1, 1, 1, 1) (c) (4,3, 1, 1, 1, 1)
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