Author, as appears in the article.: Cabrera Martínez A; Estrada-Moreno A; Rodríguez-Velázquez JA

Department: Enginyeria Informàtica i Matemàtiques

URV's Author/s: CABRERA MARTÍNEZ, ABEL / Estrada Moreno, Alejandro / Rodríguez Velázquez, Juan Alberto

Keywords: Strong differential Roman domination Quasi-total strong differential Quasi-total italian domination number Differentials in graphs strong differential quasi-total strong differential quasi-total italian domination number

Abstract: This paper is devoted to the study of the quasi-total strong differential of a graph, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. Given a vertex x ∈ V(G) of a graph G, the neighbourhood of x is denoted by N(x). The neighbourhood of a set X ⊆ V(G) is defined to be N(X) =⋃ x∈X N(x), while the external neighbourhood of X is defined to be Ne (X) = N(X) \ X. Now, for every set X ⊆ V(G) and every vertex x ∈ X, the external private neighbourhood of x with respect to X is defined as the set Pe (x, X) = {y ∈ V(G) \ X: N(y) ∩ X = {x}}. Let Xw = {x ∈ X: Pe (x, X) ̸= ∅}. The strong differential of X is defined to be ∂s (X) = |Ne (X)| − |Xw |, while the quasi-total strong differential of G is defined to be ∂s ∗ (G) = max{∂s (X): X ⊆ V(G) and Xw ⊆ N(X)}. We show that the quasi-total strong differential is closely related to several graph parameters, including the domination number, the total domination number, the 2-domination number, the vertex cover number, the semitotal domination number, the strong differential, and the quasi-total Italian domination number. As a consequence of the study, we show that the problem of finding the quasi-total strong differential of a graph is NP-hard.

Thematic Areas: Visual arts and performing arts Physics and astronomy (miscellaneous) Multidisciplinary sciences Modeling and simulation Mathematics, interdisciplinary applications Mathematics (miscellaneous) Mathematics (all) Matemática / probabilidade e estatística General mathematics Engineering (miscellaneous) Computer science (miscellaneous) Ciência da computação Chemistry (miscellaneous) Arts and humanities (miscellaneous) Architecture Applied mathematics

licence for use: https://creativecommons.org/licenses/by/3.0/es/

Author's mail: alejandro.estrada@urv.cat juanalberto.rodriguez@urv.cat

Author identifier: 0000-0001-9767-2177 0000-0002-9082-7647

Record's date: 2023-08-05

Papper version: info:eu-repo/semantics/publishedVersion

Link to the original source: https://www.mdpi.com/2073-8994/13/6/1036

Licence document URL: http://repositori.urv.cat/ca/proteccio-de-dades/

Papper original source: Symmetry-Basel. 13 (6):

APA: Cabrera Martínez A; Estrada-Moreno A; Rodríguez-Velázquez JA (2021). From the quasi-total strong differential to quasi-total italian domination in graphs. Symmetry-Basel, 13(6), -. DOI: 10.3390/sym13061036

Article's DOI: 10.3390/sym13061036

Entity: Universitat Rovira i Virgili

Journal publication year: 2021

Publication Type: Journal Publications