- Tytuł:
- All metric bases and fault-tolerant metric dimension for square of grid
- Autorzy:
-
Saha, Laxman
Basak, Mithun
Tiwary, Kalishankar - Powiązania:
- https://bibliotekanauki.pl/articles/2048644.pdf
- Data publikacji:
- 2022
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
code
resolving set
metric dimension
fault-tolerant resolving set
fault-tolerant metric dimension - Opis:
- For a simple connected graph G = (V,E) and an ordered subset W = {w1, w2, . . . , wk} of V , the code of a vertex v ∈ V , denoted by code(v), with respect to W is a k-tuple (d(v, w1), . . . , d(v, wk)), where d(v, wt) represents the distance between v and wt. The set W is called a resolving set of G if code(u) ≠ code(v) for every pair of distinct vertices u and v. A metric basis of G is a resolving set with the minimum cardinality. The metric dimension of G is the cardinality of a metric basis and is denoted by β(G). A set F ⊂ V is called fault-tolerant resolving set of G if F \ {v} is a resolving set of G for every v ∈ F. The fault-tolerant metric dimension of G is the cardinality of a minimal fault-tolerant resolving set. In this article, a complete characterization of metric bases for G2 mn has been given. In addition, we prove that the fault-tolerant metric dimension of G2 mn is 4 if m + n is even. We also show that the fault-tolerant metric dimension of G2 mn is at least 5 and at most 6 when m + n is odd.
- Źródło:
-
Opuscula Mathematica; 2022, 42, 1; 93-111
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł