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Article

General Properties on Differential Sets of a Graph

1
Faculty of Mathematics, Autonomous University of Guerrero, Carlos E. Adame 5, Col. La Garita, Acapulco 39650, Mexico
2
Department of Economy, Quantitative Methods and Economic History, Pablo de Olavide University, Carretera de Utrera Km. 1, 41013 Sevilla, Spain
*
Author to whom correspondence should be addressed.
Academic Editor: Elena Guardo
Axioms 2021, 10(4), 265; https://doi.org/10.3390/axioms10040265
Received: 4 August 2021 / Revised: 5 October 2021 / Accepted: 11 October 2021 / Published: 20 October 2021
Let G=(V,E) be a graph, and let βR. Motivated by a service coverage maximization problem with limited resources, we study the β-differential of G. The β-differential of G, denoted by β(G), is defined as β(G):=max{|B(S)|β|S|suchthatSV}. The case in which β=1 is known as the differential of G, and hence β(G) can be considered as a generalization of the differential (G) of G. In this paper, upper and lower bounds for β(G) are given in terms of its order |G|, minimum degree δ(G), maximum degree Δ(G), among other invariants of G. Likewise, the β-differential for graphs with heavy vertices is studied, extending the set of applications that this concept can have. View Full-Text
Keywords: differential; domination number; independence number differential; domination number; independence number
MDPI and ACS Style

Basilio, L.A.; Bermudo, S.; Hernández-Gómez, J.C.; Sigarreta, J.M. General Properties on Differential Sets of a Graph. Axioms 2021, 10, 265. https://doi.org/10.3390/axioms10040265

AMA Style

Basilio LA, Bermudo S, Hernández-Gómez JC, Sigarreta JM. General Properties on Differential Sets of a Graph. Axioms. 2021; 10(4):265. https://doi.org/10.3390/axioms10040265

Chicago/Turabian Style

Basilio, Ludwin A., Sergio Bermudo, Juan C. Hernández-Gómez, and José M. Sigarreta 2021. "General Properties on Differential Sets of a Graph" Axioms 10, no. 4: 265. https://doi.org/10.3390/axioms10040265

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