The 13 colonies graph is the induced subgraph of the contiguous USA graph on the 13 present-day states corresponding to the original colonies (Knuth 2025, Fig. 105). These states are Connecticut, Delaware, Georgia, Massachusetts, Maryland, North Carolina, New Hampshire, New Jersey, New York, Pennsylvania, Rhode Island, South Carolina, and Virginia. Adjacency follows the modern state boundaries used by the contiguous USA graph, rather than historical colonial boundaries.
The 13 colonies graph has vertex count 13 and edge count 18 and is outerplanar. Its chromatic number is 3. A proper coloring with three colors exists, while Connecticut, Massachusetts, and New York form a triangle graph, so two colors do not suffice.
The 13 colonies graph is graceful. It has 641952 graceful labelings, of which 160488 are distinct
up to graph automorphism and complementation
of labels (Knuth 2025, Fig. 105). Complementation replaces each label 
by 
.
The 13 colonies graph is implemented in the Wolfram Language as GraphData["ThirteenColoniesGraph"].
