Solution-Show that the block graph of any connected graph

Show that the block graph of any connected graph is a tree

Assignment Help Mathematics

Reference no: EM13928120

A. Show that the block graph of any connected graph is a tree.
Hint: Deduce the connectedness of the block graph from that of the graph itself, and its acyclicity from the maximality of each block.

B. Let e be an edge in a 2-connected graph G 6= K4. Show that either G - e or G/e is again 2-connected. Deduce a constructive characterization of the 2-connected graphs analogous to Theorem 3.2.3. and 3.2.5
Hint: Induction along Proposition 3.1.3.

Reference no: EM13928120

Questions Cloud

Create slide presentation that promotes public health : Create a 15-20 slide presentation that promotes public health. Integrate the core disciplines within public health into the presentation

Arithmetic average growth rate in dividends : Suppose Stark Ltd. just issued a dividend of $2.14 per share on its common stock. The company paid dividends of $1.80, $1.89, $1.96, and $2.07 per share in the last four years. If the stock currently sells for $60, what is your best estimate of the c..

Efficient market hypothesis : For each of the following scenarios, discuss whether profit opportunities exist from trading in the stock of the firm under the conditions that (1) the market is not weak form efficient, The stock price has risen steadily each day for the past 30 day..

What is the expected return on a portfolio-portfolio weights : A stock has a beta of 1.29 and an expected return of 12.7 percent. A risk-free asset currently earns 4.25 percent. What is the expected return on a portfolio that is equally invested in the two assets? If a portfolio of the two assets has a beta of 0..

Show that the block graph of any connected graph is a tree : Show that the block graph of any connected graph is a tree. Let e be an edge in a 2-connected graph G 6= K4. Show that either G - e or G/e is again 2-connected. Deduce a constructive characterization of the 2-connected graphs analogous to Theorem 3.2..

Explain moral and ethical considerations for governments : Explain the reason that WMDs are good for governments and why they are bad for governments. Explain moral and ethical considerations and implications for governments to consider when using WMDs

Dividend on stock-what is the current share price : Estes Park Corp. pays a constant $8.45 dividend on its stock. The company will maintain this dividend for the next 15 years and will then cease paying dividends forever. If the required return on this stock is 13 percent, what is the current share pr..

What discount rate should api apply to the cash flows : The tax rate is 40 percent. What discount rate should API apply to the cash flows from "new" projects in the Financial Services Division?

Individual employee training and career development paper : Q1. - Explain the role of training in an organization's development. Q2. - Describe different employee development methods and their benefits.

User Account

All Pages

Show that the block graph of any connected graph is a tree

Reference no: EM13928120

Reference no: EM13928120

Questions Cloud

Reviews

Write a Review

Mathematics Questions & Answers

Questions on ferris wheel

Logistic map

Finding the probability of cards

Systems of ode

Derive the boolean expression

System of equations

Linear programming problem

Find the natural domain

Introduction to numerical methods

Chart of the topological manifold

Mathematics in computing

Complex problems

Assured A++ Grade

Academics

Major Subjects

Majors

Get In Touch

TERMS & POLICIES

HELP & SUPPORT