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Simplex Graph


The simplex graph kappa(G) of an undirected graph G is the graph with vertices given by the cliques of G and edges between pairs of cliques that differ by insertion/deletion of exactly one vertex (Bandelt and van de Vel 1989, Imrich et al. 1999, Alikhani and Ghanbari 2024).

The simplex graph of every graph is a bipartite graph (Alikhani and Ghanbari 2024).

The following table sumamrizes the simplex graphs for some indexed families of graph.


See also

Clique

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References

Alikhani, S. and Ghanbari, N. "Golden Ratio in Graph Theory: A Survey." 9 Jul 2024. https://arxiv.org/abs/2407.15860.Bandelt, H.-J. and van de Vel, M. "'Embedding Topological Median Algebras in Products of Dendrons." Proc. London Math. Soc. 58, 439-453, 1989.Imrich, W.; Klavžar, S.; and Mulder, H. M. "Median Graphs and Triangle-Free Graphs." SIAM J. Disc. Math. 12, 111-118, 1999.

Cite this as:

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

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