# A note on periodicity of the 2-distance operator

Discussiones Mathematicae Graph Theory (2000)

- Volume: 20, Issue: 2, page 267-269
- ISSN: 2083-5892

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topBohdan 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 -

## References

top- [1] F. Harary, C. Hoede and D. Kadlacek, Graph-valued functions related to step graphs, J. Comb. Ing. Syst. Sci. 7 (1982) 231-246. Zbl0532.05040
- [2] E. Prisner, Graph Dynamics (Longman House, Burnt Mill, Harlow, 1995).

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