Radius-invariant graphs

Vojtech Bálint; Ondrej Vacek

Mathematica Bohemica (2004)

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

Abstract

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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 ∈ V ( G ) { e ( u ) } . A graph G is radius-edge-invariant if r ( G - e ) = r ( G ) for every e ∈ E ( G ) , radius-vertex-invariant if r ( G - v ) = r ( G ) for every v ∈ V ( G ) and radius-adding-invariant if r ( G + e ) = r ( G ) for every e ∈ E ( G ¯ ) . 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},
keywords = {radius of graph; radius-invariant graphs; radius of graph},
language = {eng},
number = {4},
pages = {361-377},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Radius-invariant graphs},
url = {http://eudml.org/doc/249405},
volume = {129},
year = {2004},
}

TY - JOUR
AU - Bálint, Vojtech
AU - Vacek, Ondrej
TI - Radius-invariant graphs
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
KW - radius of graph; radius-invariant graphs; radius of graph
UR - http://eudml.org/doc/249405
ER -

References

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  2. 10.1016/S0012-365X(03)00189-4, Discrete Math. 272 (2003), 119–126. (2003) MR2019205DOI10.1016/S0012-365X(03)00189-4
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  6. On radially extremal graphs and digraphs, a survey, Math. Bohem. 125 (2000), 215–225. (2000) Zbl0963.05072MR1768809
  7. 10.1016/0166-218X(92)90137-Y, Discrete Appl. Math. 37/38 (1992), 265–274. (1992) MR1176857DOI10.1016/0166-218X(92)90137-Y
  8. Changing and unchanging invariants for graphs, Bull. Malaysian Math. Soc. 5 (1982), 73–78. (1982) Zbl0512.05035MR0700121
  9. The number of edges in a graph of given radius, Dokl. Akad. Nauk 173 (1967), 1245–1246. (Russian) (1967) Zbl0158.42504MR0210622

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