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On Periodic Fractional (p, q)-Integral Boundary Value Problems for Sequential Fractional (p, q)-Integrodifference Equations

General Properties on Differential Sets of a Graph

Faculty of Mathematics, Autonomous University of Guerrero, Carlos E. Adame 5, Col. La Garita, Acapulco 39650, Mexico
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;
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.

AMA Style

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

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.

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