Several families of graphs are defined by having certain types of automorphisms:

In other words, the family of median graphs is closed under the retraction operation.

Several families of graphs are characterized in terms of minimum rank:

The isoperimetric problem consists of understanding how the parameters and behave for natural families of graphs.

The frequency partitions of the following families of graphs have not yet been characterized:

Many naturally occurring families of graphs are Lévy families.

For several families of graphs, the bandwidth is given by an explicit formula.

It is therefore the first in an infinite family of similarly constructed cubic graphs.

Consider a given graph and the family of undirected graphs that can be constructed by adding one or more edges from a given set.

This family of graphs possesses a number of interesting properties.