Individual Graph

Strongly Regular graph
Non planar
contains hamiltonian path but not hamiltonian cycle
Chromatic number 3
Length of shortest cycle 5

Chromatic number 3
It is both Eulerian and a penny graph (this implies that it is unit distance and planar).
It is also a 1-vertex-connected graph and a 2-edge-connected graph.

3-regular graph with 12 vertices and 18 edges.
Chromatic number 2
It is also a 3-vertex-connected and 3-edge-connected perfect graph.

It is cubic hamiltonian graph.
Can be drawn as cubic shape, it represents Planar graph
Chromatic number 3

Length of shortest cycle 3 Chromatic number 4 Properties Polyhedral Planar Chordal Perfect Treewidth 3

It also known as Hajos graph Chromatic number 4 Properties Polyhedral Planar unit distance