β-Differential of a Graph

• Main Authors: Ludwin A. Basilio, Sergio Bermudo, Jesús Leaños, José M. Sigarreta
• Format: Article
• Language: English
• Published: MDPI AG 2017-09-01
• Series: Symmetry
• Subjects: differential of a graph; domination number
• Online Access: https://www.mdpi.com/2073-8994/9/10/205
• ISSN: 2073-8994

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.