On Total Vertex Irregularity Strength of Hexagonal Cluster Graphs

Nurdin Hinding, Hye Kyung Kim, Nurtiti Sunusi and Riskawati Mise

International Journal of Mathematics and Mathematical Sciences, 2021, vol. 2021, issue 1

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 wt(x) ≠ wt(y) where wt(x) = f(x) + ∑u∈V(G)f(xu). 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 (3n2 + 1)/2.

Date: 2021
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https://doi.org/10.1155/2021/2743858

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jijmms:v:2021:y:2021:i:1:n:2743858

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