Graphs isomorphic to their path graphs

Knor, Martin, and Niepel, Ľudovít. "Graphs isomorphic to their path graphs." Mathematica Bohemica 127.3 (2002): 473-480. <http://eudml.org/doc/249058>.

@article{Knor2002,
abstract = {We prove that for every number $n\ge 1$, the $n$-iterated $P_3$-path graph of $G$ is isomorphic to $G$ if and only if $G$ is a collection of cycles, each of length at least 4. Hence, $G$ is isomorphic to $P_3(G)$ if and only if $G$ is a collection of cycles, each of length at least 4. Moreover, for $k\ge 4$ we reduce the problem of characterizing graphs $G$ such that $P_k(G)\cong G$ to graphs without cycles of length exceeding $k$.},
author = {Knor, Martin, Niepel, Ľudovít},
journal = {Mathematica Bohemica},
keywords = {line graph; path graph; cycles; line graph; path graph; cycles},
language = {eng},
number = {3},
pages = {473-480},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Graphs isomorphic to their path graphs},
url = {http://eudml.org/doc/249058},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Knor, Martin
AU - Niepel, Ľudovít
TI - Graphs isomorphic to their path graphs
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 3
SP - 473
EP - 480
AB - We prove that for every number $n\ge 1$, the $n$-iterated $P_3$-path graph of $G$ is isomorphic to $G$ if and only if $G$ is a collection of cycles, each of length at least 4. Hence, $G$ is isomorphic to $P_3(G)$ if and only if $G$ is a collection of cycles, each of length at least 4. Moreover, for $k\ge 4$ we reduce the problem of characterizing graphs $G$ such that $P_k(G)\cong G$ to graphs without cycles of length exceeding $k$.
LA - eng
KW - line graph; path graph; cycles; line graph; path graph; cycles
UR - http://eudml.org/doc/249058
ER -