Copyright © 2011 Changping Wang. 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.
A mapping is called negative if for every The maximum of the values of taken over all negative mappings , is called the modified negative decision number and is denoted by . In this paper, several sharp upper bounds of this number for a general graph are presented. Exact values of these numbers for cycles, paths, cliques and bicliques are found.