Title:

The 3pathstep operator on trees and unicyclic graphs (English) 
Author:

Zelinka, Bohdan 
Language:

English 
Journal:

Mathematica Bohemica 
ISSN:

08627959 (print) 
ISSN:

24647136 (online) 
Volume:

127 
Issue:

1 
Year:

2002 
Pages:

3340 
Summary lang:

English 
. 
Category:

math 
. 
Summary:

E. Prisner in his book Graph Dynamics defines the $k$pathstep operator on the class of finite graphs. The $k$pathstep operator (for a positive integer $k$) is the operator $S^{\prime }_k$ which to every finite graph $G$ assigns the graph $S^{\prime }_k(G)$ which has the same vertex set as $G$ and in which two vertices are adjacent if and only if there exists a path of length $k$ in $G$ connecting them. In the paper the trees and the unicyclic graphs fixed in the operator $S^{\prime }_3$ are studied. (English) 
Keyword:

3pathstep graph operator 
Keyword:

tree 
Keyword:

unicyclic graph 
MSC:

05C05 
MSC:

05C38 
idZBL:

Zbl 0995.05076 
idMR:

MR1895244 
DOI:

10.21136/MB.2002.133982 
. 
Date available:

20090924T21:57:35Z 
Last updated:

20200729 
Stable URL:

http://hdl.handle.net/10338.dmlcz/133982 
. 
Reference:

[1] F. Escalante, L. Montejano: Trees and $n$path invariant graphs, Abstract.Graph Theory Newsletter 33 (1974). 
Reference:

[2] E. Prisner: Graph Dynamics.Longman House, Burnt Mill, Harlow, 1998. MR 1379114 
. 