TY - JOUR
A2 - Solovjovs, Sergejs
AU - Hinding, Nurdin
AU - Kim, Hye Kyung
AU - Sunusi, Nurtiti
AU - Mise, Riskawati
PY - 2021
DA - 2021/01/23
TI - On Total Vertex Irregularity Strength of Hexagonal Cluster Graphs
SP - 2743858
VL - 2021
AB - For a simple graph G with a vertex set VG and an edge set EG, a labeling f:VG∪EG⟶1,2,⋯,k is called a vertex irregular total k−labeling of G if for any two different vertices x and y in VG we have wtx≠wty where wtx=fx+∑u∈VGfxu. 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 tvsG. The lower bound of tvsG 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.
SN - 0161-1712
UR - https://doi.org/10.1155/2021/2743858
DO - 10.1155/2021/2743858
JF - International Journal of Mathematics and Mathematical Sciences
PB - Hindawi
KW -
ER -