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House X Graph

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HouseXGraph

The house X graph, also called the full house 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

House Graph, Mongolian Tent Graph

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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.House of Graphs. "House X Graph." https://houseofgraphs.org/graphs/788.ISGCI: Information System on Graph Class Inclusions v2.0. "List of Small Graphs." https://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 X Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HouseXGraph.html

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