The Modified Negative Decision Number in Graphs

الملخص EN

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.