| Title:
|
The 3-path-step operator on trees and unicyclic graphs (English) |
| Author:
|
Zelinka, Bohdan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
33-40 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
E. Prisner in his book Graph Dynamics defines the $k$-path-step operator on the class of finite graphs. The $k$-path-step 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:
|
3-path-step 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:
|
2009-09-24T21:57:35Z |
| Last updated:
|
2020-07-29 |
| 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 |
| . |
