The Modified Negative Decision Number in Graphs
Changping Wang · International Journal of Mathematics and Mathematical Sciences · 2011
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∈Vx(v) taken over all negative mappings x, is called the modified negative decision number and is denoted by βD ′(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.