 Seven Bridges of Konigsberg Presented from Mathematical Perspective (2390 words)

Subject Mathematics Mathematics - Other

Question

The title of the assignment : Mathematical aspects used in the famous problem "Seven Bridges of Königsberg".

Focus is on appropriate mathematical language, mathematical presentation, personal engagement, and critical reflection.

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Introduction
The importance of the selected problem is unquestionable for at least two reasons: 1). it served as precursor of the graph theory field and 2). it is not resumed as pure theoretical subject – instead its applicability is considerable in multiple branches and domains of activity. Besides these observations the problem is valuable because it provides a way of converting real situations into solvable representations of known models.

Scope of the Paper
This paper intends to offer insight for the usage and application of graph theory in solving problems from real life. A problem like “Seven Bridges of Konigsberg” can be transformed and generalized to match practical situations using a mathematical model that is based on Euler’s study and analysis.
In summary, the formulation of the original requirement of the problem represented in Figure 1 (Weisstein) is the following: is it possible to traverse all the seven bridges in a single trip such that no bridge is used more than once and the trip has the same point for start and finish? The seven bridges are marked as aa, bb, cc, dd, ee, ff and gg.
The paper presents one way to discover if a graph has an Eulerian cycle or not without explicitly verifying all the possibilities. This approach adds more value to the original problem even if that does not have any solution (but it provides an exact answer)....

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