H Graph

"The" H graph is the tree on 6 vertices illustrated above. It is implemented in the Wolfram Language as GraphData["HGraph"].

The term "H-graph" is also used to refer to a graph expansion with the 6-vertex H graph as its base (e.g., Horton and Bouwer 1991). There are exactly two graph expansions with H-graph base that are symmetric (Biggs 1993, p. 147).

	graph	expansion
102	Biggs-Smith graph	(17; 3, 5, 6, 7)
204	cubic symmetric graph	(34; 3, 5, 7, 11)

REFERENCES

Biggs, N. L. Algebraic Graph Theory, 2nd ed. Cambridge, England: Cambridge University Press, p. 147, 1993.

Bouwer, I. Z.; Chernoff, W. W.; Monson, B.; and Star, Z. The Foster Census. Charles Babbage Research Centre, 1988.

Horton, J. D. and Bouwer, I. Z. "Symmetric Y-Graphs and H-Graphs." J. Combin. Th. Ser. B 53, 114-129, 1991.I

SGCI: Information System on Graph Class Inclusions v2.0. "List of Small Graphs." http://www.graphclasses.org/smallgraphs.html.