Constant time calculation of the metric dimension of the join of path graphs

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Tarih

2023

Yazarlar

Zhang, Chuanjun
Haidar, Ghulam
Khan, Murad ul Islam
Yousafzai, Faisal
Hila, Kostaq
Khan, Asad ul Islam

Dergi Başlığı

Dergi ISSN

Cilt Başlığı

Yayıncı

MDPI

Erişim Hakkı

info:eu-repo/semantics/openAccess

Araştırma projeleri

Organizasyon Birimleri

Organizasyon Birimi
İnsan ve Toplum Bilimleri Fakültesi, İktisat Bölümü
İktisat Bölümü, başta Türkiye ve çevre ülkeler olmak üzere küresel ekonomileri anlayan, var olan sorunları analiz ederken, iktisadi kuramları ve kavramları yetkin ve özgün bir şekilde kullanma becerisine sahip bireyler yetiştirmeyi amaçlamaktadır.

Dergi sayısı

Özet

The distance between two vertices of a simple connected graph G, denoted as (Formula presented.), is the length of the shortest path from u to v and is always symmetrical. An ordered subset (Formula presented.) of (Formula presented.) is a resolving set for G, if for ∀ (Formula presented.), there exists (Formula presented.) ∋ (Formula presented.). A resolving set with minimal cardinality is called the metric basis. The metric dimension of G is the cardinality of metric basis of G and is denoted as (Formula presented.). For the graph (Formula presented.) and (Formula presented.), their join is denoted by (Formula presented.). The vertex set of (Formula presented.) is (Formula presented.) and the edge set is (Formula presented.). In this article, we show that the metric dimension of the join of two path graphs is unbounded because of its dependence on the size of the paths. We also provide a general formula to determine this metric dimension. We also develop algorithms to obtain metric dimensions and a metric basis for the join of path graphs, with respect to its symmetries.

Açıklama

Anahtar Kelimeler

Metric Dimensions, Metric Basis, Path Graphs, Join of Graphs

Kaynak

Symmetry

WoS Q Değeri

Q2

Scopus Q Değeri

Q1

Cilt

15

Sayı

3

Künye

Zhang, C., Haidar, G., Khan, M. I., Yousafzai, F., Hila, K. ve Khan, A. I. (2023). Constant time calculation of the metric dimension of the join of path graphs. Symmetry, 15(3), 1-14. http://doi.org/10.3390/sym15030708