The paper solves one problem by E. Prisner concerning the 2-distance operator T₂. This is an operator on the class of all finite undirected graphs. If G is a graph from , 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1125,
author = {Bohdan Zelinka},
title = {A note on periodicity of the 2-distance operator},
journal = {Discussiones Mathematicae Graph Theory},
volume = {20},
year = {2000},
pages = {267-269},
zbl = {0979.05038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1125}
}
Bohdan Zelinka. A note on periodicity of the 2-distance operator. Discussiones Mathematicae Graph Theory, Tome 20 (2000) pp. 267-269. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1125/
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