Let T be the tree with Prüfer code 3, 2, 1, 3, 2, 1. (a) Give the number of vertices of T, and the number of vertices that are leaves. Justify your answers. (b) Does T contain a 3-4-walk of length 2? Justify your answer. (c) What is the number of distinct trees with vertex set V(T)? Justify your answer. (d) What is the number of distinct graphs that have T as a spanning tree? Justify your answer. (e) Give an efficient algorithm that, for any sequence d1, d2, ..., dn that is the degree sequence of a tree, constructs a particular tree with that degree sequence. Explain briefly why the algorithm is correct and efficient.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

could you please answer d and e.

 

Let T be the tree with Prüfer code 3, 2, 1, 3, 2, 1.
(a) Give the number of vertices of T, and the number of vertices that are leaves.
Justify your answers.
(b) Does T contain a 3-4-walk of length 2? Justify your answer.
(c) What is the number of distinct trees with vertex set V(T)? Justify your answer.
(d) What is the number of distinct graphs that have T as a spanning tree? Justify
your answer.
(e) Give an efficient algorithm that, for any sequence d1, d2, ..., dn that is the degree
sequence of a tree, constructs a particular tree with that degree sequence. Explain
briefly why the algorithm is correct and efficient.
Transcribed Image Text:Let T be the tree with Prüfer code 3, 2, 1, 3, 2, 1. (a) Give the number of vertices of T, and the number of vertices that are leaves. Justify your answers. (b) Does T contain a 3-4-walk of length 2? Justify your answer. (c) What is the number of distinct trees with vertex set V(T)? Justify your answer. (d) What is the number of distinct graphs that have T as a spanning tree? Justify your answer. (e) Give an efficient algorithm that, for any sequence d1, d2, ..., dn that is the degree sequence of a tree, constructs a particular tree with that degree sequence. Explain briefly why the algorithm is correct and efficient.
Expert Solution
steps

Step by step

Solved in 2 steps with 4 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,