Graph Theory: Key Terms and Definitions for Vertices, Edges, and Degree Sequences

End Vertices

If we have edge 'e', end vertices are the endpoints of that edge.

Parallel edges

Edges that have the same end vertices.

Loop

An edge where the two end vertices are the same vertex.

Simple Graph

A graph with no loops or parallel edges.

Empty Graph

A graph with no edges.

Null Graph

A graph with no vertices.

Trivial Graph

A graph with only one vertex and no edges.

Adjacent Edges

Edges that share common end vertex.

Adjacent Vertices

Vertices connected by an edge.

Pendant Vertex

A vertex with degree 1. A vertex connected to only one other vertex.

Pendant Edge

An edge whose (at least) one vertex is a pendant vertex.

Isolated Vertex

Vertex not connected to any other vertex.

Vertex Degree

Written as d(v). The number of edges going into (put of) some vertex.

Degree Sequence

Sequence of vertex degree.

Graphic sequence

There exists a simple graph with a degree sequence equal to this sequence.