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 20(2) (2000) 267-269
DOI: 10.7151/dmgt.1125

A NOTE ON PERIODICITY OF THE 2-DISTANCE OPERATOR

Bohdan Zelinka

Department of Applied Mathematics
Technical University of Liberec
Liberec, Czech Republic

To the memory of Ivan Havel

Abstract

The paper solves one problem by E. Prisner concerning the 2-distance operator T2. This is an operator on the class Cf of all finite undirected graphs. If G is a graph from Cf, then T2(G) is the graph with the same vertex set as G in which two vertices are adjacent if and only if their distance in G is 2. E. Prisner asks whether the periodicity ≥ 3 is possible for T2. In this paper an affirmative answer is given. A result concerning the periodicity 2 is added.

Keywords: 2-distance operator, complement of a graph.

2000 Mathematics Subject Classification: 05C12.

References

[1] F. Harary, C. Hoede and D. Kadlacek, Graph-valued functions related to step graphs, J. Comb. Ing. Syst. Sci. 7 (1982) 231-246.
[2] E. Prisner, Graph Dynamics (Longman House, Burnt Mill, Harlow, 1995).

Received 18 February 2000
Revised 5 July 2000