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Open AccessArticle

β-Differential of a Graph

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
(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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