Geodesic
On the simplex graph operator
Discussiones Mathematicae. Graph Theory, Tome 18 (1998) no. 2, pp. 165-169.

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A simplex of a graph G is a subgraph of G which is a complete graph. The simplex graph Simp(G) of G is the graph whose vertex set is the set of all simplices of G and in which two vertices are adjacent if and only if they have a non-empty intersection. The simplex graph operator is the operator which to every graph G assigns its simplex graph Simp(G). The paper studies graphs which are fixed in this operator and gives a partial answer to a problem suggested by E. Prisner.
Keywords: simplex of a graph, simplex operator, limit cardinal number 
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Zelinka, Bohdan. On the simplex graph operator. Discussiones Mathematicae. Graph Theory, Tome 18 (1998) no. 2, pp. 165-169. http://geodesic.mathdoc.fr/item/DMGT_1998_18_2_a2/

[1] E. Prisner, Graph dynamics, Longman House, Burnt Mill, Harlow, Essex 1995.