β-Differential of a Graph
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 ov...
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MDPI AG
2017-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/9/10/205 |
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doaj-c03aa27c0dfa42f2a0e3108e26a7bd252020-11-25T00:47:43ZengMDPI AGSymmetry2073-89942017-09-0191020510.3390/sym9100205sym9100205β-Differential of a GraphLudwin A. Basilio0Sergio Bermudo1Jesús Leaños2José M. Sigarreta3Academic Unit of Mathematics, Autonomous University of Zacatecas, Paseo la Bufa, int. Calzada Solidaridad, 98060 Zacatecas, MexicoDepartment of Economics, Quantitative Methods and Economic History, Pablo de Olavide University, Carretera de Utrera Km. 1, 41013 Sevilla, SpainAcademic Unit of Mathematics, Autonomous University of Zacatecas, Paseo la Bufa, int. Calzada Solidaridad, 98060 Zacatecas, MexicoFaculty of Mathematics, Autonomous University of Guerrero, Carlos E. Adame 5, Col. La Garita, 39350 Acapulco, Guerrero, MexicoLet 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.https://www.mdpi.com/2073-8994/9/10/205differential of a graphdomination number |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ludwin A. Basilio Sergio Bermudo Jesús Leaños José M. Sigarreta |
| spellingShingle |
Ludwin A. Basilio Sergio Bermudo Jesús Leaños José M. Sigarreta β-Differential of a Graph Symmetry differential of a graph domination number |
| author_facet |
Ludwin A. Basilio Sergio Bermudo Jesús Leaños José M. Sigarreta |
| author_sort |
Ludwin A. Basilio |
| title |
β-Differential of a Graph |
| title_short |
β-Differential of a Graph |
| title_full |
β-Differential of a Graph |
| title_fullStr |
β-Differential of a Graph |
| title_full_unstemmed |
β-Differential of a Graph |
| title_sort |
β-differential of a graph |
| publisher |
MDPI AG |
| series |
Symmetry |
| issn |
2073-8994 |
| publishDate |
2017-09-01 |
| description |
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. |
| topic |
differential of a graph domination number |
| url |
https://www.mdpi.com/2073-8994/9/10/205 |
| work_keys_str_mv |
AT ludwinabasilio bdifferentialofagraph AT sergiobermudo bdifferentialofagraph AT jesusleanos bdifferentialofagraph AT josemsigarreta bdifferentialofagraph |
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