# Article

 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 .

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