Temat: metric basis - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Closed Formulae for the Strong Metric Dimension of Lexicographic Product Graphs
Autorzy:: Kuziak, Dorota
Yero, Ismael G.
Rodríguez-Velázquez, Juan A.
Powiązania:: https://bibliotekanauki.pl/articles/31340465.pdf
Data publikacji:: 2016-11-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: strong metric dimension
strong metric basis
strong metric generator
lexicographic product graphs
Opis:: Given a connected graph G, a vertex w ∈ V (G) strongly resolves two vertices u, v ∈ V (G) if there exists some shortest u − w path containing v or some shortest v − w path containing u. A set S of vertices is a strong metric generator for G if every pair of vertices of G is strongly resolved by some vertex of S. The smallest cardinality of a strong metric generator for G is called the strong metric dimension of G. In this paper we obtain several relationships between the strong metric dimension of the lexicographic product of graphs and the strong metric dimension of its factor graphs.
Źródło:: Discussiones Mathematicae Graph Theory; 2016, 36, 4; 1051-1064
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Computing the Metric Dimension of a Graph from Primary Subgraphs
Autorzy:: Kuziak, Dorota
Rodríguez-Velázquez, Juan A.
Yero, Ismael G.
Powiązania:: https://bibliotekanauki.pl/articles/31342126.pdf
Data publikacji:: 2017-02-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: metric dimension
metric basis
primary subgraphs
rooted product graphs
corona product graphs
Opis:: Let G be a connected graph. Given an ordered set W = {w₁, . . ., w_k} ⊆ V (G) and a vertex u ∈ V (G), the representation of u with respect to W is the ordered k-tuple (d(u, w₁), d(u, w₂), . . ., d(u, w_k)), where d(u, w_i) denotes the distance between u and w_i. The set W is a metric generator for G if every two different vertices of G have distinct representations. A minimum cardinality metric generator is called a metric basis of G and its cardinality is called the metric dimension of G. It is well known that the problem of finding the metric dimension of a graph is NP-hard. In this paper we obtain closed formulae for the metric dimension of graphs with cut vertices. The main results are applied to specific constructions including rooted product graphs, corona product graphs, block graphs and chains of graphs.
Źródło:: Discussiones Mathematicae Graph Theory; 2017, 37, 1; 273-293
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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