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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:
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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