A note on signed total 2-independence in graphs

Abstract

A function f : V(G) → {-1,1} defined on the vertices of a graph G = (V, E) is a signed total 2-independence function if for each vertex v ε V(G) the sum of function values over itsopen neighborhood is at most one.The signed total 2-independence number of a graph G, denoted by α ²_st(G), is the maximum weight of a signed total 2-independence function of G. In this paper, we establish some bounds on the signed total 2-independence number for general graphs and K_r+i-free graphs.Some of our results improve or generalize previous results on the signed total 2-independence number.