Purchase Solution

Undergrad Topology Vertice Proofs

Not what you're looking for?

Ask Custom Question

1. Prove that v(Г) - e(Г) = 1 for any tree T. (v :vertices and e : edges)
2. Even better, show that v(Г) - e(Г) ≤ 1 for any graph Г, with equality precisely when Г is a tree.

Attachments
Purchase this Solution
Solution Summary

The expert examines undergrad topology vertice proofs. Proofs are analyzed.

Solution Preview

Please see attached file

1. Prove that v(Г) - e(Г) = 1for any tree T. (v :vertices and e : edges)

For the proof we need to introduce a class of special graphs. A tree G is a connected graph without cycles, i.e. any two vertices of G can be connected by a path (a sequences of edges) and there is no path whose starting and ending vertices coincide. To make a tree, we add edges beginning at some existing vertex, already counted, and extend to some new ...

Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Probability Quiz

Some questions on probability

View More Free Quizzes
Related BrainMass Solutions

  • Topology proofs

    There are several topology proofs here regarding sets, subbasis, continuity, and images.

  • Countable collections

    49368 Topology proofs This is one of the basic courses for students beginning study towards the Ph.D. degree in mathematics.

  • Continuity Proofs for Sets

    49455 Continuity proofs Show that if {Aa} is a finite collection of sets... --- (See attached file for full problem description) Please see the attached file. There are several topology proofs here regarding continuity.

  • Proofs that an Inclusion Map is Continuous

    220685 Proofs that an Inclusion Map is Continuous Show that the inclusion map i:Q -> R defined by i(q)=q for all q in Q, is continuous where both Q (rational numbers) and R(real numbers) are given the order topology.

  • Limit point proof

    Topology limit point proofs is examined.

  • Metric space and triangle inequality.

    if B is the only vertex,then project OA into the side containing O and say call it OD...Note that D is a vertice of rectangle..

  • Earl Babbie exercise using the mean and range using bivarate tables

    FREQUENCIES TABLE 1 GRAD 1 not at all 243 UNDERGRAD 1 not at all 105 GRAD 2 1-3 times 87 UNDERGRAD 2 1 -3 Times 89 GRAD 3 Monthly 24 UNDERGRAD

  • Trivial, Discrete, Cofinite, Usual and Sogenfrey Topology

    topology d) X is given the Sogenfrey topology and Y is given the usual topology e) X is given the usual topology and Y is given the Sogenfrey topology.

  • General and Differential Topology

    49380 General and Differential Topology Find conditions under which the box topology is strictly finer than the product topology. See attached file for full problem description.

View More Related Solutions