{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:15:46Z","timestamp":1760242546663,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2017,9,30]],"date-time":"2017-09-30T00:00:00Z","timestamp":1506729600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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 \u2216 D    . The differential     \u2202 ( D )     of D is defined as     | B ( D ) | \u2212 | D |    . The maximum value of     \u2202 ( D )     taken over all subsets     D \u2286 V     is the differential     \u2202 ( G )     of G. For     \u03b2 \u2208 ( \u2212 1 , \u0394 )    , the \u03b2-differential      \u2202 \u03b2   ( G )      of G is the maximum value of     { | B ( D ) | \u2212 \u03b2 | D | : D \u2286 V }    . Motivated by an influential maximization problem, in this paper we study the    \u03b2   -differential of G.<\/jats:p>","DOI":"10.3390\/sym9100205","type":"journal-article","created":{"date-parts":[[2017,10,2]],"date-time":"2017-10-02T13:10:05Z","timestamp":1506949805000},"page":"205","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["\u03b2-Differential of a Graph"],"prefix":"10.3390","volume":"9","author":[{"given":"Ludwin","family":"Basilio","sequence":"first","affiliation":[{"name":"Academic Unit of Mathematics, Autonomous University of Zacatecas, Paseo la Bufa, int. Calzada Solidaridad, 98060 Zacatecas, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergio","family":"Bermudo","sequence":"additional","affiliation":[{"name":"Department of Economics, Quantitative Methods and Economic History, Pablo de Olavide University, Carretera de Utrera Km. 1, 41013 Sevilla, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jes\u00fas","family":"Lea\u00f1os","sequence":"additional","affiliation":[{"name":"Academic Unit of Mathematics, Autonomous University of Zacatecas, Paseo la Bufa, int. Calzada Solidaridad, 98060 Zacatecas, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9","family":"Sigarreta","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, Autonomous University of Guerrero, Carlos E. Adame 5, Col. La Garita, 39350 Acapulco, Guerrero, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,9,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kempe, D., Kleinberg, J., and Tardos, E. (2003, January 24\u201327). Maximizing the spread of influence through a social network. Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, New York, NY, USA.","DOI":"10.1145\/956750.956769"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Kempe, D., Kleinberg, J., and Tardos, E. (2005, January 11\u201315). Influential nodes in a diffusion model for social networks. Proceedings of the 32nd international conference on Automata, Languages and Programming, Lisbon, Portugal.","DOI":"10.1007\/11523468_91"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Haynes, T.W., Hedetniemi, S., and Slater, P.J. (1998). 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