A note on periodicity of the 2-distance operator

• Autorzy: Bohdan Zelinka
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

2-distance operator; complement of a graph

Kategorie tematyczne

• 05C12: Distance in graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2000
• Tom: 20
• Numer: 2
• Strony: 267-269

Daty

wydano

2000

otrzymano

2000-02-18

poprawiono

2000-07-05

Twórcy

autor

Bohdan Zelinka

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

Bibliografia

• [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).

Identyfikatory

DOI

10.7151/dmgt.1125