Bounds on the signed 2-independence number in graphs
Lutz Volkmann · Discussiones Mathematicae Graph Theory · 2013
Let G be a finite and simple graph with vertex set V (G), and let f : v).The maximum of weights w(f ), taken over all signed 2-independence functions f on G, is the signed 2-independence number α 2 s (G) of G.In this work, we mainly present upper bounds on α 2 s (G), as for example, and we prove the Nordhaus-Gaddum type inequality α 2 s (G) + α 2 s (G) ≤ n + 1, where n is the order and ∆(G) is the maximum degree of the graph G.Some of our theorems improve well-known results on the signed 2-independence number.