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, wherer2s2 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 aconnected graph where the atoms of C have degree 6, H atoms have degree 2 and the Oatoms have degree 3. Show that no matter what k is, the graph is not a tree. [Hint: in any treen- m+ 1).(c) Let 7 be a finite tree on 2 or more vertices. Show that the average degree of the vertices in T isless than 2.(d) Let G be a connected graph with six vertices and the degree of each vertex is three. Find thecircuit 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) Given that, G is a connected graph Number of vertices= 6 Degree of each vertex= 3 Number of…

(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.

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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Concept explainers

Strongly Connected Components

A directed graph in which a path exists between all its pairs of vertices is called a strongly connected graph. A portion of the strongly connected directed graph that contains a path to reach from each vertex to other vertices is called a strongly connected component (SCC).

Question

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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.

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