Math Test 2

Planar Graphs

A graph that can be drawn on a flat surface with no edges crossing.

Bipartite Graphs

A graph whose vertices can be placed into two sets A and B. No connections between vertices in A and vertices in B.

Euler Circuit

A walk through the graph that uses every edge exactly once and starts and ends on the same vertex.

Euler Path

A walk through the graph that uses every edge exactly once.

Hamiltonian Circuit

A walk through the graph that uses every vertex exactly once and ends on a vertex adjacent to the starting vertex.

Hamiltonian Path

A walk through the graph that uses every vertex exactly once.

Face

An area in the plane of a graph enclosed by edges (including the outside face).

Map Coloring Theorem

Every planar graph has chromatic number less than or equal to 4.

Handshake Lemma

For any graph, the sum of the degrees of the vertices is twice the number of edges.

Isomorphic Graphs

Graphs that show the same information but are drawn differently.

Degree Sequence Theory

If two graphs do not have the same degree sequence then they cannot be isomorphic.

W(G) Clique Number

Largest copy of a complete graph within a graph G.

X(G) Chromatic Number

Minimum number of colors needed to label vertices with a color so no two adjacent vertices have the same label.

Euler's Planar Graph Formula

v-e+f=2