Graph Theory Vocab

Vertex

• a line connecting two vertices

• a point

• an edge

• an edge that starts and ends at the same vertex

Tags

CCSS.6.G.A.4

Adjacent vertices

• are connected to every other vertex in the graph

• are connected by at least one edge

• are in a loop together

• make a multigraph

A loop is when

• there is a path going from a vertex back to itself

• An edge that starts and ends at the same vertex

• if it were removed, the graph would be disconnected

• connects two vertices to each other

A path is

• an edge that starts and ends at the same vertex

• a connection between two vertices

• a series of consecutive edges in which no edge is repeated

• a complete graph

A graph is connected if

• Each vertex can reach any other vertex

• each vertex is adjacent to every other vertex

• All the vertices are odd

• the length of all the edges are equal

A graph is complete if

• every vertex is adjacent to every other vertex

• it contains at least one loop

• it has an Euler path

• it has an Euler circuit

The degree of a vertex is

• also called the order or valence

• the number of loops

• is the number of edges that connect to that vertex

• how many times it can be part of a path

An Euler Path is

• a path with loops

• a way to get from one place to another

• a path containing all edges of a graph (exactly one time)

• A path that contains all edges and starts and ends at the same point

An Euler Circuit

• is a path that starts and ends at the same vertex and contains each edge exactly one time

• is a path containing all edges of a graph (exactly once)

• is a connected graph

• in the fuse box in your house

A Multi Graph is a graph

• that contains more than one vertex

• that contains a loop or multiple edges between two vertices

• has only odd vertices

• has only even vertices