How to work out if a network is transferable

 

Some information from Wikipedia 

Leonhard Euler, born in Switzerland born 15th of April 1707 -  18th September 1783.  , physicist, astronomer, geographer, logician and engineer who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory. 

What is a Network

A network is simply a collection of connected objects. ... In mathematics, networks are often referred to as graphs, and the area of mathematics concerning the study of graphs is called graph theory.

What is a transferable Network?

A transferable network is a connections of connected objects (nodes) which are even or has two odd nodes. If the Network has more then two odd nodes then this network is not a transferable network.

Three rules for a transferable network 

Rule 1: All Nodes have to be even 

Rule 2: If their are two odd nodes this can also be considered a transferable network but you have to start and finish on the odd node

Rule 3: If their is more than two odd nodes then the network cannot be a transferable network 

An example of a transferable network 

Each node is a room and their is a robber. The robber has to try and rob each room without going down the same path twice. To figure this out this is what you can do. So as you can see from this network we have each node labelled with a letter from A to E and next to these letters are the number of edges connected to these nodes. And there are only 2 odd nodes so this means this network is considered a transferable network. And to figure out how to rob the house without going over the same path we can use the three rules. So by using rule 2 ( If their are two odd nodes this can also be considered a transferable network but you have to start and finish on the odd node) we can solve this problem by starting from A or B and finishing on A or B.

Question before you go

This is the Konigsberg bridges and my question for you is

Is this network transferable?

Comment you answer down below 

Basic shapes in terminology in mathematics

Square

As you can see this shape is a square, but how do I know this is a square? By looking at the shape I can easily say this is a square based on how the interior angles are all 90 degrees, all sides are equal and it has four sides meaning this shape is an equilateral quadrilateral shape. An equilateral quadrilateral shape has all sides equal for example a rhombus. In a square, rectangle, or rhombus, the opposite sidelines are parallel. A quadrilateral with the opposite sidelines parallel is known as a parallelogram. Another way to know if this shape is an equilateral quadrilateral shape is that from point D to point B and point C to point A both lines will be the same length. And also their midpoint will be the same. 

 

Different Triangles  There are 5 different types of triangles. First, there is an Equilateral triangle, and you can tell this is an equilateral triangle because all three sides are equal. Isosceles triangle this triangle has two equal sides and that is what makes it an Isosceles triangle and how you can tell if the triangle is Isosceles. The next triangle is the Scalene triangle, and if you want to know if this triangle is a scalene triangle it has no equal sides.  The next triangle is an Acute triangle is when it has three angles that are 90 degrees. The next triangle is a right triangle, to tell if this triangle is a right triangle is when it has one angle that is 90 degrees. And lastly, there is an Obtuse triangle where it has one angle that is 90 degrees which is similar to a right angle triangle. Do you know any more triangles? Rhombus  This shape is a Rhombus. But how do I know this is a Rhombus? Each shape has different characteristics that separate them from other shapes which are how we can find out what this shape is. It has four sides like a square but as you can see it is not. A Rhombus is a flat shape with 4 equal straight sides. A rhombus looks like a diamond. All sides have equal length. Opposite sides are parallel, and the opposite angles are equal (it is a Parallelogram). The altitude is the distance at right angles to two sides. So by using this information you can find out what a Rhombus is. Triangle  This is a triangle and you can tell because it has three equal sides and all angles add up to 180 degrees also meaning it is an equilateral triangle. An equilateral triangle is a triangle in which all three sides are equal and all internal angles are 90 degrees adding up to 180 degrees. Diamond  This is a diamond. But how do we know this is a diamond and not a Rhombus.  A diamond is a two-dimensional flat quadrilateral with four closed straight sides. A diamond is also called a rhombus because it's sides are of equal measure and because the inside opposite angles are equal. Diamonds are also considered to be parallelograms because their opposite sides are parallel to each other. So if we use this information and apply it to figuring out if this is a diamond how would we do this. You have to check if this shape has all the characteristics that are listed in this paragraph.   Rectangle  How do we know this is a rectangle and not a square? They both have interior angles of 90 degrees, four sides, and four corners but what makes this a rectangle?  The difference of a rectangle from a square is that rectangle is a quadrilateral with all four angles right angles. It follows from this that the opposite sides are parallel and of the same length. A square is a quadrilateral with all four angles right angles and all four sides of the same length. Also, both a square and a rectangle if you draw two lines from the top left corner to the bottom right corner and from the top right corner to the bottom left corner they will both be the same length.