TOPICS
Search

Tesseract Graph

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook
TesseractGraph

The skeleton of the tesseract, commonly denoted Q_4, is a quartic symmetric graph with girth 4 and diameter 4. The automorphism group of the tesseract is of order 2^7·3=384 (Buekenhout and Parker 1998). The figures above show several nice embeddings of the tesseract graph, the leftmost of which appears in Coxeter (1973) and a number of which can be found in Carr and Kocay (1999).

It is implemented in the Wolfram Language as GraphData["TesseractGraph"].

The tesseract graph is isomorphic to the 4-Hadamard graph.

It has cycle polynomial

C_(K_4)(x)=1344x^(16)+5376x^(14)+5024x^(12)+2112x^(10)+696x^8+128x^6+24x^4.
TesseractGraphLCF

The tesseract graph has two distinct generalized LCF notations of order 4, five of order 2, and four of order 1, illustrated above. The order-4 LCF notations are given by [(-7,-3),(3,7),(-3,5),(-5,3)]^4 and [(-5,-3),(3,5),(-5,5),(-5,5),(-5,5)]^4.

It has graph spectrum (-4)^1(-2)^40^62^44^1, making it an integral graph and cospectral with the Hoffman graph and meaning that neither of these two graphs is determined by spectrum.

See also

Cospectral Graphs, Determined by Spectrum, Hadamard Graph, Hoffman Graph, Hypercube, Hypercube Graph, Tesseract

Explore with Wolfram|Alpha

References

Carr, H. and Kocay, W. "An Algorithm for Drawing a Graph Symmetrically." Bull. Inst. Combin. Appl. 27, 19-25, 1999.Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, p. 123, 1973.

Cite this as:

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

Subject classifications