On Ł℘, ℘−1, …, 1 Labelings of Circulant Graphs. (19th October 2021)

• Record Type: Journal Article
• Authors: Mageshwaran, K.; Ahmad, Ali; Unyong, Bundit; Kalaimurugan, G.; Gopinath, S.
• Other Names: Tang Niansheng Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2021(2021)
• Publication Date: 2021-10-19
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2021/6578478
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : An m -Ł ℘, ℘ − 1, …, 1 labeling of a simple graph G is a mapping τ from the vertex set ∨ G to 0, 1, …, m such that τ u − τ v ≥ ℘ + 1 − d u, v, ∀ u, v ∈ ∨ G, where length of the shortest route connecting u and v is represented by d u, v . The smallest m for which there exists a m -Ł ℘, ℘ − 1, …, 1 labeling of G is known as the Ł ℘, ℘ − 1, …, 1 labeling number of G, and it is described by λ ℘ G . We define m -Ł ′ ℘, ℘ − 1, …, 1 as the same as the m -Ł ℘, ℘ − 1, …, 1 labeling if τ is one to one. The Ł ′ ℘, ℘ − 1, …, 1 labeling number of G represented by λ ℘, ℘ − 1, …, 1 ′ G and is called minimum span. In this paper, we prove that the circulant graphs with specified generating sets admit m -Ł ℘, ℘ − 1, …, 1 and m -Ł ′ ℘, ℘ − 1, …, 1 labeling and also find λ ℘ G and λ ℘, ℘ − 1, …, 1 ′ G . Moreover, we find the Ł ℘, ℘ − 1, …, 1 labeling number of any simple graph with diameter less than ℘ .