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Conditional diameter saturated graphs
Article first published online: 11 JAN 2008
DOI: 10.1002/net.20230
Copyright © 2008 Wiley Periodicals, Inc.
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Additional Information
How to Cite
Balbuena, C., García-Vázquez, P., Marcote, X. and Valenzuela, J. (2008), Conditional diameter saturated graphs. Networks, 52: 196–201. doi: 10.1002/net.20230
Publication History
- Issue published online: 18 NOV 2008
- Article first published online: 11 JAN 2008
- Manuscript Accepted:
- Manuscript Received:
Funded by
- Ministry of Education and Science, Spain
- European Regional Development Fund (ERDF). Grant Number: MTM2005-08990-CO2-02
- Andalusian Government project. Grant Number: P06-FQM-01649
- Abstract
- References
- Cited By
Keywords:
- diameter;
- conditional diameter;
- extremal graph
Abstract
The conditional diameter D��(G) of a connected graph G is a measure of the maximum distance between two subsets of vertices satisfying a given property �� of interest. For any given integer k ≥ 1, a connected graph G is said to be conditional diameter k-saturated if D��(G) ≥ k and there does not exist any other connected graph G′ with order ∣V(G′)∣ = ∣V(G)∣, size ∣E(G′)∣ > ∣E(G)∣, and conditional diameter D��(G′) ≥ k. In this article, we obtain such conditional diameter saturated graphs for a number of properties ��, generalizing the results obtained in (Ore, J Combin Theory 5(1968), 75–81) for the (standard) diameter D(G). © 2008 Wiley Periodicals, Inc. NETWORKS, 2008