# TOTAL VERTEX IRREGULARITY STRENGTH OF HAYAT TREE GRAPH

## NILAI TOTAL KETAKTERATURAN TITIK PADA GRAPH POHON HAYAT

## DOI:

https://doi.org/10.31258/jomso.v1i2.20## Keywords:

Hayat tree, Irregularity Strength, Total Vertex Irregulairty Strength, Vertex Irregular Total Labeling, Tree## Abstract

*Let G(V,E)*

*be a finite, simple graph with no loop and parallel edges.*

**V***is a set of vertices in*

**G***and*

**E***is a set edges. Labeling a graf is mapping that sends some set of graph elements to a set of positive integers. If the domain is the vertex set then the labeling is call vertex labeling, if the domain is the edge set then the labeling is call edge labeling. Define a labeling as a vertex irregular total*

**k**- labeling if for every two different vertices**x**and**y**the vertex-weight where the vertex-weigth is defined by*The minimum value of label k*

*for which*

**G***has a vertex irregular total*

*labeling is called the total vertex irregularity strength of*

**G***and denoted by*

**tvs(G)***. We consider Hayat Tree Graph, a graph as symbol of Capital of Nusantara (IKN) which is ratified by president in June 2023. In this paper, we determined the total vertex irregularity strength of Hayat Tree Graph.*

* *

## References

A. Ahmad, K. M. Awan, L. Javaid, Slamin, Total vertex irregularity strength of wheel related graphs, Australasian Journal of Combinatorics, 51 (2011), 147-156.

A. Krishnaa, Some Applications of Labelled Graphs, International Journalof Mathematics and Trends and Technology, 37, 209-2013.

Bača et al., On irregular total labelling, Discrete Mathematics, 307(2007), 1378-1388.

D. Indriati, W.I.E. Wijayanti, K. A. Sugeng, M.Baca, A. Semanicova-Fenovcikova, The total vertex irregularity strength of generalized helm graphs and prism with outer pendant edges, Australasian Journal of Combinatorics, 65 (1) (2016), 14-26.

Hedge, S. M. (2007). Labelled Graph and Its Application. The International Conference on Graph Theory and Information Security

Nurdin, E.T. Baskoro, A. N. M. Salman. N. N. Gaos, On the total vertex irregularity strength of trees, Discrete Mathematics, 310 (2010), 3043-3048.

Nurdin, E. T. Baskoro, A. N. M. Salman, N. N. Gaos, On the total vertex irregular labelings for several types of trees, Util, Math, 23 (2009), 511-516.

Prasanna, N. L., Sravanthi, K., dan Sudhakar, N. (2014). Applications of Graph Labeling in Communication Networks. Computer Science Journal.

R. Simanjuntak, Susilawati, E.T. Baskoro, Total vertex irregularity strength of trees with many vertices of degree two, Electronic Journal of Graph Theory & Applications 8 (2) (2020), 415-421.

Sudibyo, N.A. Pelabelan Total Tak Reguler pada Beberapa Graf, Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP). Vol. 10 No. 2 (2018), 9-16.

Susilawati, E.T. Baskoro, R. Simanjuntak., Total vertex Irregularity strength of trees with maximum degree four, AIP Conference Proceedings 1707 (1) (2016), 1-7.

Susilawati, E.T. Baskoro, R. Simanjuntak, Total vertex irregularity strength of trees with maximum degree five, Electronic Journal of Graph Theory & Applications 6 (2) (2018).

Susilawati, E.T. Baskoro, R. Simanjuntak, On the vertex irregular total labeling for subdivision of trees, Australasian Journal of Combinatorics 71 (2) (2018), 293-302.

Varkey, M.T.K dan Kumar, R.T.J. (2015). Even Graceful Labelling of a Class of Trees. International Journal on Applications of Graph Theory in Wireless Ad hoc Networks and Sensor Networks(GRAPH-HOC), 7(4)