مشخصات پژوهش

A signed bad function of G is a function f : V (G) → {−1, 1} such that f(N[v]) ≤ 1 for every v ∈ V (G) where N[v] is the closed neighborhood of v. The signed bad number is βs(G) =max{Pv∈V (G) f(v) | f is a signed bad function of G}. Ghameshlou et al. [A. N. Ghameshlou, A. Khodkar and S. M. Sheikholeslami, The signed bad numbers in graphs, Discrete Math. Algorithms Appl. 1 (2011) 33–41] proved that for any bipartite graph of order n, βs(G) ≤ n + 2 − 2 √ n+ 2. But their proof has a gap and the bound is not correct in general. In this note, we modify their proof and show that for any bipartite graph of order n, βs(G) ≤ n + 6 − 2 √ 9 + 2n, and also we characterize the bipartite graphs attaining this bound