Pigeonhole Theorem
Balls can’t fit in preoccupied spots or whatever
Handshaking Theorem
Every undirected graph has twice the vertices for the amount of edges
Graph:
has to have every vertex forming at least one edge, and every edge has 1 or 2 vertices connected to it
Pseudographs:
may include loops or overlapping edges on vertices
Complete Graph:
Exactly one edge between every two vertices (like the Israel star thingy or a box shape with an X in the middle, or a triangle, or a line)
Cycle Graph:
Same as Complete graph but empty from the inside (has to be connected to each other such as an empty box, and a triangle is actually both complete and a cycle)
Wheel Graph:
Same as cycle with a vertex in the middle connected to all of the outer vertices
Trees:
Connected, undirected, no simple circuit (not a cycle that’s for sure)
Forest:
Same but not connected, can have multiple trees within (they have to
M-ary tree:
every leave has no more than m children
A tree with n vertices has n-1 edges
root is level 0
balanced: roots same height or h-1