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(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|-(vl-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|-(vl-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
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
Problem 1PE
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D, e, f ASAP. 

 

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.
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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