Euler Path Problem : The Seven Bridges of Konigsberg

In Konigsberg, Germany, a river ran through the city such that in its center was an island, and after passing the island, the river broke into two parts. Seven bridges were built so that the people of the city could get from one part to another. A crude map of the center of Konigsberg might look like this:

The people wondered whether or not one could walk around the city in a way that would involve crossing each bridge exactly once.

In the graph, the vertex1 represents the island, which is connected to the lands by 5 bridges, vertices 2, 3 and 4 represent the lands. This graph has 7 edges, which represent the 7 bridges.
Our goal is now into trying to find a path which goes through all 7 edges ...

Solution Summary

A euler path problem is solved. The solution is detailed and well presented.

1. Determine which of the reflexive, symmetric, and transitive properties are satisfied by the given relation R defined over set S. See Appendix A for the definition of reflexive, symmetric, and transitive properties.
S={1,2,3} and R={(1,1), (1,2), (2,1), (2,2)}
Appendix A Definition
A relation R on a set S may have any of t

Page 90, Theorem 4.6 ( To show that a digraph is hamiltonian if and only if for each vertex v, indegree (v) =outdegree (v)
Page 92 Exercise problem 4.1 ( A modified version of konigsbergproblem where, two extra bridges are built. )
Page 93, Figure 4.5 need to show as Hamilton. (Show that dodecahedron is hami

4.4 Prove Let D be a nontrivial connected digraph. Then D is Eulerian if and only if
od(v)=id(v) for every vertex v of D.
Od means the outdegree of a vertex v of a digraph D. (is the number of vertices of D that are adjacent from v.
id means the indegree of a vertex v of a digraph D.( is the number of vertices of D adjace

Please show all working. You may tabulate your solutions.
a. Use the explicit Euler to simulate two steps of the system...
See attached for full problem description.

I need help using Euler an the improved Euler methods: (look at attachment for better formula display)
1. Consider the initial value problem y' = 2xy, y(1) = 1. Use theEuler's method and improved Euler's method with h = 0.1and h = 0.05 to obtain approximate values of the solution at x = 1.5. At each step compare the approxim

(Please see the attached file for the complete problem description)
Show that theproblem of finding geodesics on a surface g(x,y,z) = 0 joining points (x_1,y_1,z_1) and (x_2,y_2,z_2) can be found by obtaining the minimum of:
(please see the attached file)
Hence find the geodesics for the parabolic cylinder y = x^2.
Pleas

Truth tables are related to Euler circles. Arguments in the form of Euler circles can be translated into statements using the basic connectives and the negation as follows:
Let p be "The object belongs to set A." Let q be "the object belongs to set B."
All A is B is equivalent to p -> q
No A is B is equivalent to p -> ~q

For this problem it helps to know that: 3x7x13 = 273
(a) Define theEuler Totient function, (SYMBOL)
For (b) to (f) please see attached.
(PLEASE SEE ATTACHMENT FOR COMPLETE PROBLEM AND PROPER SYMBOLS)