Intro to Graph Theory | Definitions & Ex: 7 Bridges of Konigsberg

Leonhard Euler, a famous 18th century mathematician, founded graph theory by studying a problem called the 7 bridges of Konigsberg. Could one travel over a connection of landmasses and bridges hitting each bridge exactly once? This motivated abstract study and graph theory was born.

We formally define the concept of a graph, and talk about how to form graphs form real world examples. Finally we introduce the idea of a “Graph Isomorphism” which loosely says that if we keep the same vertices and edges (but maybe relabel them) then we can move their configuration around when drawing as much as we like as long as all the relationships are the same. The more precise technical definition is the following:

A Graph Isomorphism between two graphs (V1, E1) and (V2,E2) is a bijective function f from V1 to V2 such that any two vertices a and b in V1 have an edge in E1 connecting them if and only if f(a) and f(b) have an edge in E2 connecting them.

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