Mathematica Bohemica (2004)

• Volume: 129, Issue: 4, page 361-377
• ISSN: 0862-7959

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## Abstract

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The eccentricity $e\left(v\right)$ of a vertex $v$ is defined as the distance to a farthest vertex from $v$. The radius of a graph $G$ is defined as a $r\left(G\right)={min}_{u\in V\left(G\right)}\left\{e\left(u\right)\right\}$. A graph $G$ is radius-edge-invariant if $r\left(G-e\right)=r\left(G\right)$ for every $e\in E\left(G\right)$, radius-vertex-invariant if $r\left(G-v\right)=r\left(G\right)$ for every $v\in V\left(G\right)$ and radius-adding-invariant if $r\left(G+e\right)=r\left(G\right)$ for every $e\in E\left(\overline{G}\right)$. Such classes of graphs are studied in this paper.

## How to cite

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Bálint, Vojtech, and Vacek, Ondrej. "Radius-invariant graphs." Mathematica Bohemica 129.4 (2004): 361-377. <http://eudml.org/doc/249405>.

@article{Bálint2004,
abstract = {The eccentricity $e(v)$ of a vertex $v$ is defined as the distance to a farthest vertex from $v$. The radius of a graph $G$ is defined as a $r(G)=\min _\{u \in V(G)\}\lbrace e(u)\rbrace$. A graph $G$ is radius-edge-invariant if $r(G-e)=r(G)$ for every $e \in E(G)$, radius-vertex-invariant if $r(G-v)= r(G)$ for every $v \in V(G)$ and radius-adding-invariant if $r(G+e)=r(G)$ for every $e \in E(\overline\{G\})$. Such classes of graphs are studied in this paper.},
author = {Bálint, Vojtech, Vacek, Ondrej},
journal = {Mathematica Bohemica},
language = {eng},
number = {4},
pages = {361-377},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
url = {http://eudml.org/doc/249405},
volume = {129},
year = {2004},
}

TY - JOUR
AU - Bálint, Vojtech
AU - Vacek, Ondrej
JO - Mathematica Bohemica
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 129
IS - 4
SP - 361
EP - 377
AB - The eccentricity $e(v)$ of a vertex $v$ is defined as the distance to a farthest vertex from $v$. The radius of a graph $G$ is defined as a $r(G)=\min _{u \in V(G)}\lbrace e(u)\rbrace$. A graph $G$ is radius-edge-invariant if $r(G-e)=r(G)$ for every $e \in E(G)$, radius-vertex-invariant if $r(G-v)= r(G)$ for every $v \in V(G)$ and radius-adding-invariant if $r(G+e)=r(G)$ for every $e \in E(\overline{G})$. Such classes of graphs are studied in this paper.
LA - eng
UR - http://eudml.org/doc/249405
ER -

## References

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