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Open AccessArticle

β-Differential of a Graph

Academic Unit of Mathematics, Autonomous University of Zacatecas, Paseo la Bufa, int. Calzada Solidaridad, 98060 Zacatecas, Mexico
Department of Economics, Quantitative Methods and Economic History, Pablo de Olavide University, Carretera de Utrera Km. 1, 41013 Sevilla, Spain
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;
Received: 12 September 2017 / Revised: 26 September 2017 / Accepted: 26 September 2017 / Published: 30 September 2017
(This article belongs to the Special Issue Graph Theory)
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
Keywords: differential of a graph; domination number differential of a graph; domination number
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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.

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