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Open AccessArticle

# β-Differential of a Graph

by Ludwin A. Basilio 1, Sergio Bermudo 2, Jesús Leaños 1 and José M. Sigarreta 3,*
1
Academic Unit of Mathematics, Autonomous University of Zacatecas, Paseo la Bufa, int. Calzada Solidaridad, 98060 Zacatecas, Mexico
2
Department of Economics, Quantitative Methods and Economic History, Pablo de Olavide University, Carretera de Utrera Km. 1, 41013 Sevilla, Spain
3
Faculty of Mathematics, Autonomous University of Guerrero, Carlos E. Adame 5, Col. La Garita, 39350 Acapulco, Guerrero, Mexico
*
Author to whom correspondence should be addressed.
Symmetry 2017, 9(10), 205; https://doi.org/10.3390/sym9100205
Received: 12 September 2017 / Revised: 26 September 2017 / Accepted: 26 September 2017 / Published: 30 September 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. View Full-Text
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MDPI and ACS Style

Basilio, L.A.; Bermudo, S.; Leaños, J.; Sigarreta, J.M. β-Differential of a Graph. Symmetry 2017, 9, 205.