A note on periodicity of the 2-distance operator

Bohdan Zelinka. "A note on periodicity of the 2-distance operator." Discussiones Mathematicae Graph Theory 20.2 (2000): 267-269. <http://eudml.org/doc/270506>.

@article{BohdanZelinka2000,
abstract = {The paper solves one problem by E. Prisner concerning the 2-distance operator T₂. This is an operator on the class $C_f$ of all finite undirected graphs. If G is a graph from $C_f$, 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.},
author = {Bohdan Zelinka},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {2-distance operator; complement of a graph; diameter},
language = {eng},
number = {2},
pages = {267-269},
title = {A note on periodicity of the 2-distance operator},
url = {http://eudml.org/doc/270506},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Bohdan Zelinka
TI - A note on periodicity of the 2-distance operator
JO - Discussiones Mathematicae Graph Theory
PY - 2000
VL - 20
IS - 2
SP - 267
EP - 269
AB - The paper solves one problem by E. Prisner concerning the 2-distance operator T₂. This is an operator on the class $C_f$ of all finite undirected graphs. If G is a graph from $C_f$, 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.
LA - eng
KW - 2-distance operator; complement of a graph; diameter
UR - http://eudml.org/doc/270506
ER -