https://padlet.com/luke_tunstall/qw55b723n7d4 Made with ♥ en-us 2017-07-28 21:08:30 UTC 2025-12-30 14:27:57 UTC hello@padlet.com https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662873 Leonard Euler is the father of graph theory

]]> 2017-07-28 21:39:26 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662873 https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662879 Graph Theory was first known to "officially exist" in the mid-1800's]]> 2017-07-28 21:39:39 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662879 https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662888 A graph is made of vertices and the edges that connect vertices to each other. ]]> 2017-07-28 21:40:01 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662888 https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662899 Unlike Eulerian Circuits, Hamiltonian Circuits focus on trying to visit each vertex exactly once, and can have edges traveled multiple times. While Eulerain Circuits and Paths have characteristics that can help one solve a Eulerian Problem, Hamiltonian paths do not. This makes them more difficult to find as one usually must find them through luck, or trail and error.]]> 2017-07-28 21:40:24 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662899 https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662904 Eulerian paths and Circuits

]]> 2017-07-28 21:40:42 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662904 https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662907 Many graphs can be drawn on a piece of paper so that the edges intersect only at the vertices. This kind of graph is called a planar graph. Non-planar graphs have edges that intersect basically anywhere on the graphs, not just on the vertices.]]> 2017-07-28 21:40:47 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662907 https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662921 Paths travel along edges and vertices to connect a pair of vertices together.]]> 2017-07-28 21:41:05 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662921 https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662950 if all of the vertices on a graph are even, this graph is an Eulerian circuit.]]> 2017-07-28 21:42:33 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662950 https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662992 Graphs are complete when each pair of vertices is connected by exactly one edge.]]> 2017-07-28 21:44:13 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662992 https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662995 2017-07-28 21:44:20 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179662995 https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179663007 A bipartite graph is a graph whose the vertices can be separated into two sets so that each line/edge on the graph can connect a vertex in the first set to a vertex in the second.

]]> 2017-07-28 21:44:55 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179663007 https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179663009 If an edge connects two vertices than that edge is an incident to those two vertices. The degree of a vertex is the number of edges that are incident to that vertex. So, if  edges are incident to a vertex, then that vertex is an even vertex. If three edges are incident to a vertex, then that vertex is an odd vertex.]]> 2017-07-28 21:44:56 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179663009 https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179663029 Eulerian Path is a path that cover all of the edges or paths only once.
If you look at the graph besides this and see the numbers as steps, you can see that the path that it makes a path without going over the same path once]]> 2017-07-28 21:45:48 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179663029 https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179663102 Euler had been visiting a town named Königsberg in Prussia, when he was confronted with the problem that is now known as  the Königsberg Bridge Problem. This is what got him thinking about what is now called graph theory. 

]]> 2017-07-28 21:48:42 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179663102 https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179663178 Eulerian paths on graphs with one odd vertex must end and begin at that vertex.
Eulerian paths on graphs with two odd vertices must end and begin and one odd vertex and end at the other.
Eulerian paths don't exist on graphs with more than two odd vertices.
Graphs with an odd number of odd vertices do not exist.]]> 2017-07-28 21:51:53 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179663178 https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179663192 Circuit is a path that goes starts and ends at a same vertex or point.
This is kinda like an electrical circuit]]> 2017-07-28 21:52:23 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179663192 https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179663232 2017-07-28 21:54:21 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179663232 https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179663258 2017-07-28 21:55:19 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179663258 https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179663271 2017-07-28 21:55:37 UTC https://padlet.com/luke_tunstall/qw55b723n7d4/wish/179663271