Diameter-invariant graphs

Ondrej Vacek

Mathematica Bohemica (2005)

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

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 ( 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.

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 -

References

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  10. Design of diameter e -invariant networks, Congr. Numerantium 65 (1988), 89–102. (1988) Zbl0800.05011MR0992859
  11. Three classes of diameter e -invariant graphs, Comment. Math. Univ. Carolin. 28 (1987), 227–232. (1987) MR0904748
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  13. 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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