The 3-path-step operator on trees and unicyclic graphs

Zelinka, Bohdan. "The 3-path-step operator on trees and unicyclic graphs." Mathematica Bohemica 127.1 (2002): 33-40. <http://eudml.org/doc/249026>.

@article{Zelinka2002,
abstract = {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.},
author = {Zelinka, Bohdan},
journal = {Mathematica Bohemica},
keywords = {3-path-step graph operator; tree; unicyclic graph; 3-path-step graph operator; tree; unicyclic graph},
language = {eng},
number = {1},
pages = {33-40},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The 3-path-step operator on trees and unicyclic graphs},
url = {http://eudml.org/doc/249026},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Zelinka, Bohdan
TI - The 3-path-step operator on trees and unicyclic graphs
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 1
SP - 33
EP - 40
AB - 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.
LA - eng
KW - 3-path-step graph operator; tree; unicyclic graph; 3-path-step graph operator; tree; unicyclic graph
UR - http://eudml.org/doc/249026
ER -