Note on upper bound signed 2-independence in digraphs

Abstract

Let D be a finite digraph with the vertex set V(D) and arc set A(D). A two-valued function f : V(D) → {−1,1} defined on the vertices of a digraph D is called a signed 2-independence function if f(N−[v]) ≤ 1 for every v in D. The weight of a signed 2-independence function is f (V (D)) = [수식] f (v). The maximum weight of a signed 2-independence function of D is the signed 2-independence number α_s^2(D) of D. Recently, Volkmann [3] began to investigate this parameter in di- graphs and presented some upper bounds on α^2_s(D) for general digraph D. In this paper, we improve upper bounds on α_s^2(D) given by Volkmann [3].