See below file.

**Subject Computer Science Discrete Math**

See below file.

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

1. First of all we prove that in any connected planar graph it holds the following inequality: e≤3*v-6.

Sum of the degrees for faces is twice the number of edges; also each face has the degree at least 3. From these findings => 2*e≥3*f .

But Euler’s formula => v-e+f=2 => f = e-v+2 => 3f=3e-3v+6 and using the above result=> 2e≥3e-3v+6 => 3v≥ e+6....

Sum of the degrees for faces is twice the number of edges; also each face has the degree at least 3. From these findings => 2*e≥3*f .

But Euler’s formula => v-e+f=2 => f = e-v+2 => 3f=3e-3v+6 and using the above result=> 2e≥3e-3v+6 => 3v≥ e+6....

This is only a preview of the solution. Please use the purchase button to see the entire solution

Prime Numbers, Numeration Bases & Euclidean Algorithm

$18.00

GCD

Euclidean Algorithm

Prime

Base

Division

Binary

Octal

Hexadecimal

Computer Science

Discrete Math

10 Problems with Functions, Sets, Recurrence Relations, Modular Operations, and Equivalence

$75.00

Recurrence

Relation

Set

Operation

Function

One-to-one

Onto

Rule

Counterexample

Intersection

Union

Difference

Subset

Mod

Fibonacci

Sequence

Induction

Equivalence

Relation

Reflexive

Symmetric

Transitive

Class

Recurrence

Relation

Set

Operation

Function

One-to-one

Onto

Rule

Counterexample

Intersection

Union

Difference

Subset

Mod

Fibonacci

Sequence

Induction

Equivalence

Relation

Reflexive

Symmetric

Transitive

Class

Discrete Math Exercises with Functions

$10.00

Function

Domain

Range

Solution

One-to-one

Onto

Set

Target

Equation

Codomain

Computer Science

Discrete Math

Discrete Math Questions

$10.00

Recurrence

Array

Arithmetic

Sequence

Progression

Polynomial

Relation

Generating

Function