Towaco Post Office: An Euler Circuit

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Miranda Pesci Essay #1 Sue Smith (Towaco Post Office) Dear Sue, As per our phone conversation I am sending you the information we discussed in greater detail. Like I stated previously a tour that starts at a vertex of a graph and visits each vertex once and only once, returning to where it started, is called a Hamiltonian Circuit. A circuit that covers each edge of a graph once and only once is called an Euler Circuit. It is much easier to determine if a graph has an Euler circuit as opposed to a Hamiltonian circuit. For our purposes your route has an Euler circuit and I will now explain how I came to that conclusion. The first step in discovering an Euler circuit in a graph is to determine if its valances are even. The valance of

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