International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 245405 | https://doi.org/10.1155/S0161171203212059

John Holliday, Peter Johnson, "Shields-Harary numbers of graphs with respect to continuous concave cost functions", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 245405, 10 pages, 2003. https://doi.org/10.1155/S0161171203212059

Shields-Harary numbers of graphs with respect to continuous concave cost functions

Received06 Dec 2002

Abstract

The Shields-Harary numbers are a class of graph parameters that measure a certain kind of robustness of a graph, thought of as a network of fortified reservoirs, with reference to a given cost function. We prove a result about the Shields-Harary numbers with respect to concave continuous cost functions which will simplify the calculation of these numbers for certain classes of graphs, including graphs formed by two intersecting cliques, and complete multipartite graphs.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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