Metric dimensions of bicyclic graphs
Yükleniyor...
Dosyalar
Tarih
2023
Yazarlar
Khan, Asad
Haidar, Ghulam
Abbas, Naeem
Khan, Murad ul Islam
Niazi, Azmat Ullah Khan
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
MDPI
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
The distance d(va, vb) between two vertices of a simple connected graph G is the length of the shortest path between va and vb. Vertices va, vb of G are considered to be resolved by a vertex v if d(va, v) 6= d(vb, v). An ordered set W = fv1, v2, v3, . . . , vsg V(G) is said to be a resolving set for G, if for any va, vb 2 V(G), 9 vi 2 W 3 d(va, vi) 6= d(vb, vi). The representation of vertex v with respect to W is denoted by r(vjW) and is an s-vector(s-tuple) (d(v, v1), d(v, v2), d(v, v3), . . . , d(v, vs)). Using representation r(vjW), we can say that W is a resolving set if, for any two vertices va, vb 2 V(G), we have r(vajW) 6= r(vbjW). A minimal resolving set is termed a metric basis for G. The cardinality of the metric basis set is called the metric dimension of G, represented by dim(G). In this article, we study the metric dimension of two types of bicyclic graphs. The obtained results prove that they have constant metric dimension.
Açıklama
Anahtar Kelimeler
Graph Theory, Bicyclic Graph, Metric Basis, Resolving Set, Metric Dimensions
Kaynak
Mathematics
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
11
Sayı
4
Künye
Khan, A., Haidar, G., Khan, M. I., Niazi, A. U. K. ve Khan, A. I. (2023). Metric dimensions of bicyclic graphs. Mathematics, 11(4), 1-17. https://doi.org/10.3390/math11040869
