Deltoidal Icositetrahedral Graph

The deltoidal icositetrahedral graph is an Archimedean dual graph which is the skeleton of the deltoidal icositetrahedron. It is implemented in the Wolfram Language as GraphData["DeltoidalIcositetrahedralGraph"].

The plots above show the adjacency matrices, incidence matrices, and graph distance matrices for the deltoidal icositetrahedral graph.

The following table summarizes some properties of the graph.

property	value
automorphism group order	48
characteristic polynomial
chromatic number	2
chromatic polynomial	?
claw-free	no
clique number	2
determined by spectrum	?
diameter	6
distance regular	no
dual graph name	small rhombicuboctahedral graph
edge chromatic number	4
edge connectivity	3
edge count	48
Eulerian	no
girth	4
Hamiltonian	no
Hamiltonian cycle count	0
Hamiltonian path count	0
independence number	14
integral	no
line graph	?
perfect matching graph	no
planar	yes
polyhedral graph	yes
radius	4
regular	no
square-free	no
traceable	no
triangle-free	yes
vertex connectivity	3
vertex count	26