International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 62, Pages 3921-3930

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

John Holliday and Peter Johnson

Department of Discrete and Statistical Sciences, Auburn University, Auburn 36849, AL, USA

Received 6 December 2002

Copyright © 2003 John Holliday and Peter Johnson. 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.


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.