The Modified Negative Decision Number in Graphs

A mapping x : V → {−1, 1} is called negative if∑u∈N v x u ≤ 1 for every v ∈ V. The maximum of the values of ∑ v∈V x v taken over all negative mappings x, is called the modified negative decision number and is denoted by β′ D G . 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.