Articles producció científica> Enginyeria Informàtica i Matemàtiques

The adjacency dimension of graphs

  • Identification data

    Identifier: imarina:9293726
    Handle: https://hdl.handle.net/20.500.11797/imarina9293726
    Authors:
    S BermudoJM RodríguezJA Rodríguez-VelázquezJM Sigarreta
    Abstract:
    It is known that the problem of computing the adjacency dimension of a graph is NP-hard. This suggests finding the adjacency dimension for special classes of graphs or obtaining good bounds on this invariant. In this work we obtain general bounds on the adjacency dimension of a graph G in terms of known parameters of G. We discuss the tightness of these bounds and, for some particular classes of graphs, we obtain closed formulae. In particular, we show the close relationships that exist between the adjacency dimension and other parameters, like the domination number, the location-domination number, the 2-domination number, the independent 2-domination number, the vertex cover number, the independence number and the super domination number.

  • Others:

    Author, as appears in the article.: S Bermudo; JM Rodríguez; JA Rodríguez-Velázquez; JM Sigarreta
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: Rodríguez Velázquez, Juan Alberto
    Keywords: Super domination number Metric dimension Location-domination number Independence number Adjacency dimension
    Abstract: It is known that the problem of computing the adjacency dimension of a graph is NP-hard. This suggests finding the adjacency dimension for special classes of graphs or obtaining good bounds on this invariant. In this work we obtain general bounds on the adjacency dimension of a graph G in terms of known parameters of G. We discuss the tightness of these bounds and, for some particular classes of graphs, we obtain closed formulae. In particular, we show the close relationships that exist between the adjacency dimension and other parameters, like the domination number, the location-domination number, the 2-domination number, the independent 2-domination number, the vertex cover number, the independence number and the super domination number.
    Thematic Areas: Theoretical computer science Mathematics, applied Mathematics Matemática / probabilidade e estatística Geometry and topology Discrete mathematics and combinatorics Algebra and number theory
    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/publishedVersion
    Link to the original source: https://amc-journal.eu/index.php/amc/article/view/2496
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Papper original source: Ars Mathematica Contemporanea. 22 (3), # P3. 02-16 pp. (3):
    APA: S Bermudo; JM Rodríguez; JA Rodríguez-Velázquez; JM Sigarreta (2022). The adjacency dimension of graphs. Ars Mathematica Contemporanea, 22 (3), # P3. 02-16 pp.(3), -. DOI: 10.26493/1855-3974.2496.07a
    Article's DOI: 10.26493/1855-3974.2496.07a
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2022
    Publication Type: Journal Publications

  • Keywords:

    Algebra and Number Theory,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematics,Mathematics, Applied,Theoretical Computer Science
    Super domination number
    Metric dimension
    Location-domination number
    Independence number
    Adjacency dimension
    Theoretical computer science
    Mathematics, applied
    Mathematics
    Matemática / probabilidade e estatística
    Geometry and topology
    Discrete mathematics and combinatorics
    Algebra and number theory

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