Lemke Graph

The Lemke graph is the 8-node graph with 13 edges illustrated above (Lemke and Kleitman 1989, Hurlbert 2011, Hurlbert 2013).

The Lemke graph is the smallest graph that does not have a property related to the pebbling number known as the 2-pebbling property (Hurlbert 2013).

REFERENCES

Hurlbert, G. "A Linear Optimization Technique for Graph Pebbling." 28 Jan 2011.

 https://arxiv.org/abs/1101.5641.Hurlbert, G. "General Graph Pebbling." Disc. Appl. Math. 161, 1221-1231, 2013.

Hurlbert, G. "Graph Pebbling." In Handbook of Graph Theory (Ed. J. L. Gross, J. Yellen, and P. Zhang). Kalamazoo, MI: Chapman and Hall/CRC, 1428-1449, 2013.

Lemke, P. and Kleitman, D. J. "An Addition Theorem on the Integers Modulo ." J. Number Th. 31, 335-345, 1989.