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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1072,
author = {Bohdan Zelinka},
title = {On the simplex graph operator},
journal = {Discussiones Mathematicae Graph Theory},
volume = {18},
year = {1998},
pages = {165-169},
zbl = {0930.05084},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1072}
}
Bohdan Zelinka. On the simplex graph operator. Discussiones Mathematicae Graph Theory, Tome 18 (1998) pp. 165-169. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1072/
[000] [1] E. Prisner, Graph dynamics, Longman House, Burnt Mill, Harlow, Essex 1995.