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Applicable Algebra in Engineering, Communication and Computing

Erschienen in:

26.10.2021 | Original Paper

Metric dimension of complement of annihilator graphs associated with commutative rings

verfasst von: Sh. Ebrahimi, R. Nikandish, A. Tehranian, H. Rasouli

Erschienen in: Applicable Algebra in Engineering, Communication and Computing | Ausgabe 6/2023

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Abstract

For a connected graph G(V, E) a set of vertices \(S\subseteq V(G)\) resolves the graph G, and S is a resolving set of G, if every vertex is uniquely determined by its vector of distances to the vertices of S. A resolving set S of minimum cardinality is a metric basis for G, and the number of elements in the resolving set of minimum cardinality is the metric dimension of G. Let R be a commutative ring with non-zero identity. The annihilator graph of R, denoted by AG(R), is the (undirected) graph whose vertex set is the set of all non-zero zero-divisors of R and two distinct vertices x and y are adjacent if and only if \(ann_R(xy)\ne ann_R(x)\cup ann_R(y)\). In this paper, the metric dimension of the complement of AG(R) is studied and some metric dimension formulae for this graph are given.

Vorheriger Artikel Interleavings and matchings as representations

Nächster Artikel Two-valued cross correlation distributions between binary m sequences and their decimation sequences

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Titel: Metric dimension of complement of annihilator graphs associated with commutative rings
verfasst von: Sh. Ebrahimi
R. Nikandish
A. Tehranian
H. Rasouli
Publikationsdatum: 26.10.2021
Verlag: Springer Berlin Heidelberg
Erschienen in: Applicable Algebra in Engineering, Communication and Computing / Ausgabe 6/2023
Print ISSN: 0938-1279
Elektronische ISSN: 1432-0622
DOI: https://doi.org/10.1007/s00200-021-00533-4

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