# Diameter-invariant graphs

Mathematica Bohemica (2005)

• Volume: 130, Issue: 4, page 355-370
• ISSN: 0862-7959

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## Abstract

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The diameter of a graph $G$ is the maximal distance between two vertices of $G$. A graph $G$ is said to be diameter-edge-invariant, if $d\left(G-e\right)=d\left(G\right)$ for all its edges, diameter-vertex-invariant, if $d\left(G-v\right)=d\left(G\right)$ for all its vertices and diameter-adding-invariant if $d\left(G+e\right)=d\left(e\right)$ for all edges of the complement of the edge set of $G$. This paper describes some properties of such graphs and gives several existence results and bounds for parameters of diameter-invariant graphs.

## How to cite

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Vacek, Ondrej. "Diameter-invariant graphs." Mathematica Bohemica 130.4 (2005): 355-370. <http://eudml.org/doc/249594>.

@article{Vacek2005,
abstract = {The diameter of a graph $G$ is the maximal distance between two vertices of $G$. A graph $G$ is said to be diameter-edge-invariant, if $d(G-e)=d(G)$ for all its edges, diameter-vertex-invariant, if $d(G-v)=d(G)$ for all its vertices and diameter-adding-invariant if $d(G+e)=d(e)$ for all edges of the complement of the edge set of $G$. This paper describes some properties of such graphs and gives several existence results and bounds for parameters of diameter-invariant graphs.},
author = {Vacek, Ondrej},
journal = {Mathematica Bohemica},
keywords = {extremal graphs; diameter of graph; distance; extremal graph; diameter of graph; distance},
language = {eng},
number = {4},
pages = {355-370},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Diameter-invariant graphs},
url = {http://eudml.org/doc/249594},
volume = {130},
year = {2005},
}

TY - JOUR
AU - Vacek, Ondrej
TI - Diameter-invariant graphs
JO - Mathematica Bohemica
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 130
IS - 4
SP - 355
EP - 370
AB - The diameter of a graph $G$ is the maximal distance between two vertices of $G$. A graph $G$ is said to be diameter-edge-invariant, if $d(G-e)=d(G)$ for all its edges, diameter-vertex-invariant, if $d(G-v)=d(G)$ for all its vertices and diameter-adding-invariant if $d(G+e)=d(e)$ for all edges of the complement of the edge set of $G$. This paper describes some properties of such graphs and gives several existence results and bounds for parameters of diameter-invariant graphs.
LA - eng
KW - extremal graphs; diameter of graph; distance; extremal graph; diameter of graph; distance
UR - http://eudml.org/doc/249594
ER -

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