On critical and cocritical radius edge-invariant graphs

• Autorzy: Ondrej Vacek
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

extremal graphs; radius of graph

Kategorie tematyczne

• 05C12: Distance in graphs
• 05C35: Extremal problems

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2008
• Tom: 28
• Numer: 3
• Strony: 393-418

Daty

wydano

2008

otrzymano

2006-09-11

poprawiono

2007-12-18

zaakceptowano

2008-06-06

Twórcy

autor

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

Bibliografia

• [1] V. Bálint and O. Vacek, Radius-invariant graphs, Math. Bohem. 129 (2004) 361-377.
• [2] F. Buckley and F. Harary, Distance in Graphs (Addison-Wesley, Redwood City, 1990).
• [3] R.D. Dutton, S.R. Medidi and R.C. Brigham, Changing and unchanging of the radius of graph, Linear Algebra Appl. 217 (1995) 67-82, doi: 10.1016/0024-3795(94)00153-5.
• [4] F. Gliviak, On radially extremal graphs and digraphs, a survey, Math. Bohem. 125 (2000) 215-225.
• [5] S.M. Lee, Design of diameter e-invariant networks, Congr. Numer. 65 (1988) 89-102.
• [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.
• [7] O. Vacek, Diameter-invariant graphs, Math. Bohem. 130 (2005) 355-370.
• [8] V.G. Vizing, On the number of edges in graph with given radius, Dokl. Akad. Nauk 173 (1967) 1245-1246 (in Russian).
• [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.

Identyfikatory

DOI

10.7151/dmgt.1415