Author, as appears in the article.: Cabrera Martinez, A; Rodriguez-Velazquez, J A
Department: Enginyeria Informàtica i Matemàtiques
URV's Author/s: CABRERA MARTÍNEZ, ABEL / Rodríguez Velázquez, Juan Alberto
Keywords: Roman domination number Roman domination Perfect roman domination Perfect domination Perfect differential of a graph Differential of a graph
Abstract: Let G be a graph of order n(G) and vertex set V(G). Given a set S subset of V(G), we define the perfect neighbourhood of S as the set N-p(S) of all vertices in V(G)\S having exactly one neighbour in S. The perfect differential of S is defined to be partial differential partial derivative(p)(S) = vertical bar N-p(S)vertical bar - vertical bar S vertical bar. In this paper, we introduce the study of the perfect differential of a graph, which we define as partial derivative(p)(G) = max{partial derivative(p)(S): S subset of V(G)}. Among other results, we obtain general bounds on partial derivative(p)(G) and we prove a Gallai-type theorem, which states that partial differential partial derivative(p)(G) + gamma(p)(R)(G) = n(G), where gamma(p)(R)(G) denotes the perfect Roman domination number of G. As a consequence of the study, we show some classes of graphs satisfying a conjecture stated by Bermudo
Thematic Areas: Mathematics (miscellaneous) Mathematics Matemática / probabilidade e estatística
licence for use: https://creativecommons.org/licenses/by/3.0/es/
Author's mail: juanalberto.rodriguez@urv.cat
Author identifier: 0000-0002-9082-7647
Record's date: 2024-10-26
Papper version: info:eu-repo/semantics/submittedVersion
Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
Papper original source: Quaestiones Mathematicae. 45 (3): 327-345
APA: Cabrera Martinez, A; Rodriguez-Velazquez, J A (2022). ON THE PERFECT DIFFERENTIAL OF A GRAPH. Quaestiones Mathematicae, 45(3), 327-345. DOI: 10.2989/16073606.2020.1858992
Entity: Universitat Rovira i Virgili
Journal publication year: 2022
Publication Type: Journal Publications
Repositori URV