{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T20:38:42Z","timestamp":1774643922214,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,5,6]],"date-time":"2020-05-06T00:00:00Z","timestamp":1588723200000},"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>If     G = ( V ( G ) , E ( G ) )     is a simple connected graph with the vertex set     V ( G )     and the edge set     E ( G )    , S is a subset of     V ( G )    , and let     B ( S )     be the set of neighbors of S in     V ( G ) \u2216 S    . Then, the differential of S    \u2202 ( S )     is defined as     | B ( S ) | \u2212 | S |    . The differential of G, denoted by     \u2202 ( G )    , is the maximum value of     \u2202 ( S )     for all subsets     S \u2286 V ( G )    . The graph operator     Q ( G )     is defined as the graph that results by subdividing every edge of G once and joining pairs of these new vertices iff their corresponding edges are incident in G. In this paper, we study the relations between     \u2202 ( G )     and     \u2202 (  Q ( G )  )    . Besides, we exhibit some results relating the differential     \u2202 ( G )     and well-known graph invariants, such as the domination number, the independence number, and the vertex-cover number.<\/jats:p>","DOI":"10.3390\/sym12050751","type":"journal-article","created":{"date-parts":[[2020,5,7]],"date-time":"2020-05-07T04:46:07Z","timestamp":1588826767000},"page":"751","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["The Differential on Graph Operator Q(G)"],"prefix":"10.3390","volume":"12","author":[{"given":"Ludwin","family":"Basilio","sequence":"first","affiliation":[{"name":"Academic Unit of Mathematics, Autonomous University of Zacatecas, Paseo la Bufa, int. Calzada Solidaridad, Zacatecas 98060, Mexico"}]},{"given":"Jair","family":"Simon","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, Autonomous University of Guerrero, Carlos E. Adame 5, Col. La Garita 39650, Acapulco, Guerrero, Mexico"}]},{"given":"Jes\u00fas","family":"Lea\u00f1os","sequence":"additional","affiliation":[{"name":"Academic Unit of Mathematics, Autonomous University of Zacatecas, Paseo la Bufa, int. Calzada Solidaridad, Zacatecas 98060, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8909-1978","authenticated-orcid":false,"given":"Omar","family":"Cayetano","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, Autonomous University of Guerrero, Carlos E. Adame 5, Col. La Garita 39650, Acapulco, Guerrero, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,6]]},"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. 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