(d) Let G be a connected graph with six vertices and the degree of each vertex is three. Find the circuit rank of G. [hint: circuit rank = |E|-(|v|-1)]. (e) Let F be a forest with n vertices and k components. Show that F has n-k edges. (f) Draw all nonisomorphic trees on six vertices.
(d) Let G be a connected graph with six vertices and the degree of each vertex is three. Find the circuit rank of G. [hint: circuit rank = |E|-(|v|-1)]. (e) Let F be a forest with n vertices and k components. Show that F has n-k edges. (f) Draw all nonisomorphic trees on six vertices.
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Please do d, e and f
![Question 3
(a) Suppose that T is a tree with n vertices, two of which have degrees and s, respectively, where
r2s22. Prove that 7'has at least r+s-2 vertices of degree one.
(b) An alcohol molecule has formula CAH24-20 where k is a positive integer. The molecule is a
connected graph where the atoms of C have degree 6, H atoms have degree 2 and the O
atoms have degree 3. Show that no matter what k is, the graph is not a tree. [Hint: in any tree
n=m+1].
(c) Let 7' be a finite tree on 2 or more vertices. Show that the average degree of the vertices in T'is
less than 2.
(d) Let G be a connected graph with six vertices and the degree of each vertex is three. Find the
circuit rank of G. [hint: circuit rank = |E|-(|v|-1)].
(e) Let F be a forest with n vertices and k components. Show that F has n-k edges.
(f) Draw all nonisomorphic trees on six vertices.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F913df25b-8a64-4f59-9fb6-9874a4fa75b7%2F3dbdfe94-2cd0-4191-8e4c-f27ddd2c765b%2Fw67maf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 3
(a) Suppose that T is a tree with n vertices, two of which have degrees and s, respectively, where
r2s22. Prove that 7'has at least r+s-2 vertices of degree one.
(b) An alcohol molecule has formula CAH24-20 where k is a positive integer. The molecule is a
connected graph where the atoms of C have degree 6, H atoms have degree 2 and the O
atoms have degree 3. Show that no matter what k is, the graph is not a tree. [Hint: in any tree
n=m+1].
(c) Let 7' be a finite tree on 2 or more vertices. Show that the average degree of the vertices in T'is
less than 2.
(d) Let G be a connected graph with six vertices and the degree of each vertex is three. Find the
circuit rank of G. [hint: circuit rank = |E|-(|v|-1)].
(e) Let F be a forest with n vertices and k components. Show that F has n-k edges.
(f) Draw all nonisomorphic trees on six vertices.
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