β-Differential of a Graph
Ludwin A. Basilio, Sergio Bermudo, Jesús Leaños, José M. Sigarreta · Symmetry · 2017
Let G = ( V , E ) be a simple graph with vertex set V and edge set E. Let D be a subset of V, and let B ( D ) be the set of neighbours of D in V ∖ D . The differential ∂ ( D ) of D is defined as | B ( D ) | − | D | . The maximum value of ∂ ( D ) taken over all subsets D ⊆ V is the differential ∂ ( G ) of G. For β ∈ ( − 1 , Δ ) , the β-differential ∂ β ( G ) of G is the maximum value of { | B ( D ) | − β | D | : D ⊆ V } . Motivated by an influential maximization problem, in this paper we study the β -differential of G.