Signed Total 2-Independence in Graphs

摘要

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 the sum of its function values over any open neighborhood is at most one. That is, for every v e V, f(N(v)) < 1, where N(v) consists of every vertex adjacent to v. The weight of a signed total 2-independence function is ,f(V) = ^2f(v), over all vertices v G V. The signed total 2-independence number of a graph G, denoted by o%t(G), is the maximum weight of a signed total 2-independence function of G. In this paper, we establish some upper bounds on a2st{G) of G, and a sharp upper bound on a2st(G) for an r-partite graph G with minimum degree <5(G) > 2.