# On critical and cocritical radius edge-invariant graphs

Discussiones Mathematicae Graph Theory (2008)

- Volume: 28, Issue: 3, page 393-418
- ISSN: 2083-5892

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topOndrej Vacek. "On critical and cocritical radius edge-invariant graphs." Discussiones Mathematicae Graph Theory 28.3 (2008): 393-418. <http://eudml.org/doc/270696>.

@article{OndrejVacek2008,

abstract = {The concepts of critical and cocritical radius edge-invariant graphs are introduced. We prove that every graph can be embedded as an induced subgraph of a critical or cocritical radius-edge-invariant graph. We show that every cocritical radius-edge-invariant graph of radius r ≥ 15 must have at least 3r+2 vertices.},

author = {Ondrej Vacek},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {extremal graphs; radius of graph; critical radius edge invariant graph; cocritical radius edge invariant graph},

language = {eng},

number = {3},

pages = {393-418},

title = {On critical and cocritical radius edge-invariant graphs},

url = {http://eudml.org/doc/270696},

volume = {28},

year = {2008},

}

TY - JOUR

AU - Ondrej Vacek

TI - On critical and cocritical radius edge-invariant graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2008

VL - 28

IS - 3

SP - 393

EP - 418

AB - The concepts of critical and cocritical radius edge-invariant graphs are introduced. We prove that every graph can be embedded as an induced subgraph of a critical or cocritical radius-edge-invariant graph. We show that every cocritical radius-edge-invariant graph of radius r ≥ 15 must have at least 3r+2 vertices.

LA - eng

KW - extremal graphs; radius of graph; critical radius edge invariant graph; cocritical radius edge invariant graph

UR - http://eudml.org/doc/270696

ER -

## References

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- [6] S.M. Lee and A.Y. Wang, On critical and cocritical diameter edge-invariant graphs, Graph Theory, Combinatorics, and Applications 2 (1991) 753-763. Zbl0841.05081
- [7] O. Vacek, Diameter-invariant graphs, Math. Bohem. 130 (2005) 355-370. Zbl1112.05033
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- [9] H.B. Walikar, F. Buckley and K.M. Itagi, Radius-edge-invariant and diameter-edge-invariant graphs, Discrete Math. 272 (2003) 119-126, doi: 10.1016/S0012-365X(03)00189-4. Zbl1029.05044

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