(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.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Can you please help me with d,e, and f

Ouestion 3
(a) Suppose that T is a tree with n vertices, two of which have degrees r and s, respectively, where
r2s2 2. Prove that Thas at least r+s-2 vertices of degree one.
(b) An alcohol molecule has formula C,H220 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.
Transcribed Image Text:Ouestion 3 (a) Suppose that T is a tree with n vertices, two of which have degrees r and s, respectively, where r2s2 2. Prove that Thas at least r+s-2 vertices of degree one. (b) An alcohol molecule has formula C,H220 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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