On the Signed (Total) K-Independence Number in Graphs

Abstract

Let G be a graph. A function f : V (G) → {−1, 1} is a signed k- independence function if the sum of its function values over any closed neighborhood is at most k − 1, where k ≥ 2. The signed k-independence number of G is the maximum weight of a signed k-independence function of G. Similarly, the signed total k-independence number of G is the maximum weight of a signed total k-independence function of G. In this paper, we present new bounds on these two parameters which improve some existing bounds.

Keywords

• domination in graphs
• signed k-independence
• limited packing
• tuple domination