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# Graph Theory

Graph theory is a relatively new type of math and probably gained fame when Leonhard Euler solved the famous Seven Bridges of Konigsberg problem.

A graph is a nonempty finite set of vertices V along with a set E of 2-element subsets of V. The elements of V are called vertices, the elements of E are called edges. To put it simply, all a graph is, is dots and lines connecting them.

In the above graph the vertices would be $$1,2,3,4,5,6$$. And the notation for the set of vertices is $$V=\lbrace 1,2,3,4,5,6\rbrace$$.
An example of one edge $$($$2 dots with a line between them$$)$$ in the above graph is $$\lbrace 2,5\rbrace$$. The notation representing all the edges is $$E=\left\{\left\{2,5\right\},\left\{2,6\right\},\left\{3,4\right\},\left\{3,5\right\}\left\{3,6\right\},\left\{4,5\right\},\left\{4,6\right\},\left\{5,6\right\}\right\}$$.