# The Seven Bridges of Königsberg

The Seven Bridges of Königsberg is a historically notable problem in mathematics. It goes like this.

1. Accessing any bridge without crossing to its other end

# What does this have anything to do with Graph Theory?

Well, Euler observed that…

## 1. Choice of land route within each land mass is irrelevant.

This implied that the problem needn’t be viewed photographically or in a map, but can be expressed in an abstract form.

## 2. If one enters by a bridge, one must leave by a bridge.

Euler observed that except at the endpoints of the walk, when one enters a vertex by a bridge, one must exit the vertex by a bridge. That is the number of times one enters a non-terminal vertex equals the number of times one leaves it. Now, if every bridge can be walked upon just once, then for each vertex ( the non-terminal ones) the number of bridges touching that land mass must be even, that is the degree of each node should be even(half of them towards,half away from the land)

# Some defintions:

A Graph is an ordered triplet G=(V(G), E(G), ψ(G)) consisting of non-empty set V(G) of vertices, a set E(G) of edges and an incidence function ψ(G) that associates with each edge of G with an un-ordered pair of vertices.

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## Enfa Rose George

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Sipping my coffee in a warm cafe, a book in hand, waiting for my DL model to finish training