TOPICS
Search

House Graph


HouseGraph

The house graph is a simple graph on 5 nodes and 6 edges, illustrated above in two embeddings, whose name derives from its resemblance to a schematic illustration of a house with a roof. It is implemented in the Wolfram Language as GraphData["HouseGraph"].

HouseXGraph

The house X-graph is the house graph plus the two edges connecting diagonally opposite vertices of the square base, illustrated above. It is also one of the two graphs obtained by removing two edges from the pentatope graph K_5 (the other being the W_5 wheel graph). It is implemented in the Wolfram Language as GraphData["HouseXGraph"].


See also

Mongolian Tent Graph

Explore with Wolfram|Alpha

References

Barrus, M. D.; Hartke, S. G.; and Kumbhat, M. "Graph Classes Characterized Both by Forbidden Subgraphs and Degree Sequences." Nov. 17, 2005. http://www.math.uiuc.edu/~hartke/math/papers/degseqforcing.pdf.Brandstädt, A.; Le, V. B.; and Spinrad, J. P. Graph Classes: A Survey. Philadelphia, PA: SIAM, p. 18, 1987.ISGCI: Information System on Graph Class Inclusions v2.0. "List of Small Graphs." http://www.graphclasses.org/smallgraphs.html.West, D. B. Introduction to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, p. 12, 2000.

Cite this as:

Weisstein, Eric W. "House Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HouseGraph.html

Subject classifications