DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 18(2) (1998) 165-169
DOI: 10.7151/dmgt.1072

ON THE SIMPLEX GRAPH OPERATOR

Bohdan Zelinka

Department of Applied Mathematics
Faculty of Education, Technical University of Liberec
Voronežská 13, 461 17 Liberec
Czech Republic

e-mail: bohdan.zelinka@vslib.cz

Abstract

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.

1991 Mathematics Subject Classification: 05C75.

References

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

Received 15 October 1997
Revised 18 March 1998