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Discussiones Mathematicae Graph Theory 28(3) (2008) 393-418
DOI: https://doi.org/10.7151/dmgt.1415

ON CRITICAL AND COCRITICAL RADIUS EDGE-INVARIANT GRAPHS

Ondrej Vacek

Department of Mathematics and Descriptive Geometry
Faculty of Wood Sciences and Technology
Technical University Zvolen
T.G. Masaryka 24, 960 53 Zvolen, Slovak Republic
e-mail: o.vacek@vsld.tuzvo.sk

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.

Keywords: extremal graphs, radius of graph.

2000 Mathematics Subject Classification: 05C12, 05C35.

References

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Received 11 September 2006
Revised 18 December 2007
Accepted 6 June 2008