Pentatope Graph


The pentatope graph is the skeleton of the pentatope, namely the complete graph K_5. It is sometimes also known as the Kuratowski graph (Nikolić et al. 2000, p. 281).

Since the n-simplex has graph spectrum n^1(-1)^n (Cvetkovic et al. 1998, p. 72; Buekenhout and Parker 1998), the pentatope graph is an integral graph with graph spectrum 4^1(-1)^4. The order of its automorphism group is |Aut(G)|=120. The pentatope graph is the line graph of the star graph S_6.

See also

Complete Graph, Pentatope

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Nikolić, S.; Trinajstić, N.; and Mihalić, A. "The Detour Matrix and the Detour Index." Ch. 6 in Topological Indices and Related Descriptors in QSAR and QSPR (Ed. J. Devillers A. T. and Balaban). Amsterdam, Netherlands: Gordon and Breach, pp. 279-306, 2000.

Referenced on Wolfram|Alpha

Pentatope Graph

Cite this as:

Weisstein, Eric W. "Pentatope Graph." From MathWorld--A Wolfram Web Resource.

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