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Graph Theory Eulerian and Hamiltonian Graphs

Graph TheoryEulerian and Hamiltonian GraphsAimTo introduce Eulerian and Hamiltonian OutcomesAt the end of this section you will: Know what an Eulerian Graph is, Know what a Hamiltonian Graph GraphsThe following problem , often referred to as the bridges of K onigsberg problem , was firstsolved by Euler in the eighteenth century. The problem was rather simple the townof K onigsberg consists of two islands and seven bridges. Is it possible, by beginninganywhere and ending anywhere, to walk through the town by crossing all seven bridgesbut not crossing any bridge twice?Figure 1: The bridges of K onigsberg problemWe will first present some definitions and then present a theorem that Euler used toshow that it is in fact impossible to walk through the town and traverse all the bridgesonly trail:AnEulerian trailis a trail that visits every edge of the Graph onceand only once.

problem because there exists within the graph more than 2 vertices of odd degree. Question: Are either of the following graphs traversable - if so, graph the solution trail of the graph? 2. Graph Theory Hamiltonian Graphs Hamiltonian Circuit: A Hamiltonian circuit in a …

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