ISSN 1234-3099 (print version)
ISSN 2083-5892 (electronic version)
SCImago Journal Rank (SJR) 2018: 0.763
Rejection Rate (2017-2018): c. 84%
Mathematicae Graph Theory 20(2) (2000) 267-269 DOI: 10.7151/dmgt.1125
Department of Applied Mathematics
Technical University of Liberec
Liberec, Czech Republic
To the memory of Ivan Havel
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
Keywords: 2-distance operator, complement of a graph.
2000 Mathematics Subject Classification: 05C12.
Received 18 February 2000
Revised 5 July 2000