On Total Vertex Irregularity Strength of Hexagonal Cluster Graphs. (23rd January 2021)

• Record Type: Journal Article
• Authors: Hinding, Nurdin; Kim, Hye Kyung; Sunusi, Nurtiti; Mise, Riskawati
• Other Names: Solovjovs Sergejs Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2021(2021)
• Publication Date: 2021-01-23
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2021/2743858
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : For a simple graph G with a vertex set V G and an edge set E G, a labeling f : V G ∪ ​ E G ⟶ 1, 2, ⋯, k is called a vertex irregular total k − labeling of G if for any two different vertices x and y in V G we have w t x ≠ w t y where w t x = f x + ∑ u ∈ V G f x u . The smallest positive integer k such that G has a vertex irregular total k − labeling is called the total vertex irregularity strength of G, denoted by tvs G . The lower bound of tvs G for any graph G have been found by Baca et. al. In this paper, we determined the exact value of the total vertex irregularity strength of the hexagonal cluster graph on n cluster for n ≥ 2 . Moreover, we show that the total vertex irregularity strength of the hexagonal cluster graph on n cluster is 3 n 2 + 1 / 2 .