Euler

Graph Theory Eulerian and Hamiltonian Graphs

Graph Theory Eulerian Circuit: An Eulerian circuit is an Eulerian trail that is a circuit. That is, it begins and ends on the same vertex. Eulerian Graph: A graph is called Eulerian when it contains an Eulerian circuit. Figure 2: An example of an Eulerian trial.

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Chapter 6: Graph Theory

Leonhard Euler first discussed and used Euler paths and circuits in 1736. Rather than finding a minimum spanning tree that visits every vertex of a graph, an Euler path or circuit can be used to find a way to visit every edge of a graph once and only once. This would be useful for checking parking meters along the streets of a city, patrolling the

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The Seven Bridges of Konigsberg-Euler's solution

Special Euler's properties To get the Euler path a graph should have two or less number of odd vertices. Starting and ending point on the graph is a odd vertex. Problem faced A vertex needs minimum of two edges to get in and out. If a vertex has odd edges then

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On numbers which are the sum of two ... - The Euler Archive

Leonhard Euler 1. Arithmeticians are accustomed to investigating the nature of numbers in many ways where they show their source, either by addition or by multiplication. Of the aforementioned kind, the simplest is composition from units, by which all integers are understood to arise from units. Then numbers can also thus be

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Euler Equations - University of Alabama in Huntsville

Euler equations. 19.1 Second-Order Euler Equations Basics A second-order differential equation is called anEuler equation if it can be written as αx2y′′ + βxy′ + γy = 0 where α, β and γ are constants (in fact, we will assume they are real-valued constants). For example, x2y′′ − 6xy′ + …

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Design of Columns

1 Design of Columns Introduction According to ACI Code 2.2, a structural element with a ratio of height-to-least lateral dimension exceeding three used primarily to support compressive loads is defined as column. Columns support vertical loads from the floor and roof slabs and transfer these loads to the footings.