Graph properties and parameters

A selection of parameters supported by the software:

Encodings

Different formats to encode or describe a graph.

• adjacency matrix
• incidence matrix
• distance matrix
• graph6 format

Degree

Properties related to the vertex degree of a graph.

• regular
• biregular
• strongely regular
• split graph

Distance

Parameters in the context of graph distance.

• diameter
• radius

Connectedness

Different values concerning connectivity or components of a graph.

• vertex connectivity
• edge connectivity
• hamilton connected
• number of connected components

Colouring

Topological graph parameters e.g. for graph colouring or domination.

• bipartite
• chromatic number
• vertex critical
• edge critical
• chromatic index
• perfect
• class 1
• total chromatic number
• domination number
• number of vertex colourings

Paths and Cycles

Existence, number, or length of paths and cycles in a graph.

• hamiltonian
• hypohamiltonian
• traceable
• hypotraceable
• eulerian
• tree
• girth
• number of hamiltonian circuits
• number of hamiltonian paths
• length of longest path
• length of longest cycle
• cycle length vector
• intersection of all longest paths

Subgraphs

Existence of special subgraphs in the graph.

• perfect matching (1-factorable)
• number of perfect matchings (1-factors)
• every vertex is on a triangle
• clique number
• independence number
• block graph

Forbidden Subgraphs

Non-existence of special subgraphs in the graph.

• C4-free
• triangle-free
• claw-free
• chordal

Automorphisms

Properties in the context of graph automorphism.

• vertex transitive
• edge transitive
• self-complementary
• number of automorphisms