β-Differential of a Graph

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, ∆), 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.