Graphs and Trees

Subgraph

A graph whose vertices and edges are a subset of another

Cycle

A path that can be repeated b/c it has no one beginning or end

Loop

An edge that begins and ends at the same vertex

Digraph

Each edge has a direction

Directed

Each edge has a direction

Complete Graph

Every pair of vertices is connected by an edge

Eulerian (path or cycle)

Goes through every edge on the path once

Connected

If there is at least one path between every pair of vertices

Edge (branch)

Line connecting two vertices

Multigraph

More than one edge between vertices

Outdegree

Number of edges that originate at the vertex

Indegree

Number of edges that terminate at the vertex

Hamiltonian (path or cycle)

Passes through every vertex of a graph once and only once

Vertex (node)

Point

Simple Digraph

Simple directed graph, but can have one edge in each direction between vertices

Simple Graph

Single edge between vertices and no loops

Degree of a vertex

The number of edges for which the vertex is one of the vertices that define the edge

Path

The sequence of vertices

Tree

Undirected graph where any 2 vertices are connected by exactly one path

Adjacent Vertices

Vertices that have an edge between them

Undirected

When there are no arrows