On the Total Vertex Irregularity Strength of Series Parallel Graph sp(m,r,3)

Authors

  • Corry Corazon Marzuki Universitas Islam Negeri Sultan Syarif Kasim Riau, Pekanbaru, Indonesia
  • Muzdhalifah Marinka Utami Universitas Islam Negeri Sultan Syarif Kasim Riau, Pekanbaru, Indonesia
  • Fitri Aryani Universitas Islam Negeri Sultan Syarif Kasim Riau, Pekanbaru, Indonesia
  • Mona Elviyenti Politechnic Caltex Riau, Pekanbaru, Indonesia
  • Ade Novia Rahma Universitas Islam Negeri Sultan Syarif Kasim Riau, Pekanbaru, Indonesia

DOI:

https://doi.org/10.30983/lattice.v5i2.10483

Keywords:

Series parallel graph, Total vertex irregularity strength, Total vertex irregular labelling

Abstract

This paper addresses the problem of determining the total vertex irregularity strength of the series-parallel graph family  for  and. The total vertex irregularity strength  of a graph  is defined as the smallest integer  such that there exists a total k-labelling  where the vertex weights  are distinct for each vertex. The graph family  is generated through repeated series and parallel compositions, with parameters and a fixed structural parameter 3. To solve this problem, we construct an explicit total labelling that ensures distinct vertex weights, providing an upper bound for . Additionally, we perform a structural analysis of the graph, which yields a matching lower bound. The results demonstrate that the total vertex irregularity strength of  is given by . This work contributes a new insight into the characterization of the total vertex irregularity strength for this specific class of graphs, providing both upper and lower bounds for .   Penelitian ini membahas permasalahan dalam menentukan nilai total ketakteraturan titik pada keluarga graf seri-paralel  untuk  dan . Nilai total ketakteraturan titik  untuk suatu graf  didefinisikan sebagai nilai minimum  sehingga terdapat pelabelan total  dengan bobot titik  yang berbeda untuk setiap titik. Keluarga graf  dibangun melalui komposisi seri dan paralel secara berulang, dengan parameter  dan parameter struktur tetap 3. Untuk menyelesaikan masalah ini, kami mengonstruksi pelabelan total eksplisit yang memastikan bobot titik saling berbeda, sehingga menghasilkan batas atas untuk . Selain itu, kami melakukan analisis struktur graf untuk memperoleh batas bawah yang sesuai. Hasil penelitian ini menunjukkan bahwa total vertex irregularity strength untuk  diberikan oleh . Penelitian ini memberikan kontribusi berupa wawasan baru dalam karakterisasi nilai total ketakteraturan titik untuk kelas graf ini, dengan menyediakan batas atas dan batas bawah untuk

Author Biographies

Muzdhalifah Marinka Utami, Universitas Islam Negeri Sultan Syarif Kasim Riau, Pekanbaru

Department of Mathematics

Fitri Aryani, Universitas Islam Negeri Sultan Syarif Kasim Riau, Pekanbaru

Department of Mathematics

Mona Elviyenti, Politechnic Caltex Riau, Pekanbaru

Electronical Telecomunication Department

Ade Novia Rahma, Universitas Islam Negeri Sultan Syarif Kasim Riau, Pekanbaru

Department of Mathematics

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Published

2025-12-30

How to Cite

Marzuki, C. C., Utami, M. M., Aryani, F., Elviyenti, M., & Rahma, A. N. (2025). On the Total Vertex Irregularity Strength of Series Parallel Graph sp(m,r,3). Lattice Journal : Journal of Mathematics Education and Applied, 5(2), 160–175. https://doi.org/10.30983/lattice.v5i2.10483

Issue

Vol. 5 No. 2 (2025): Desember 2025

Section

Articles

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Copyright (c) 2025 Corry Corazon Marzuki, Muzdhalifah Marinka Utami, Fitri Aryani, Mona Elviyenti, Ade Novia Rahma

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