ON THE TOTAL VERTEX IRREGULARITY STRENGTH OF SERIES PARALLEL GRAPH sp(m,r,4)

  • Corry Corazon Marzuki Mathematics Department, Islamic State University Sultan Syarif Kasim Riau, Indonesia
  • Aminah Utami Mathematics Department, Islamic State University Sultan Syarif Kasim Riau, Indonesia
  • Mona Elviyenti Electronica and Communications Department, Polytechnic Caltex Riau, Indonesia
  • Yuslenita Muda Mathematics Department, Islamic State University Sultan Syarif Kasim Riau, Indonesia
DOI: https://doi.org/10.30598/barekengvol18iss1pp0213-0222
Keywords: Series Parallel Graph, Total Vertex Irregularity Strength, Total Vertex Irregular Labeling

Abstract

his study aims to determine the total vertex irregularity strength on a series parallel graph for  and . Total labeling is said to be vertex irregular, if the weights for each vertices are different. Determination of the total vertex irregularity of series parallel graph is done by obtaining the largest lower bound and the smallest upper bound. The lower bound is obtained by analyzing the structure of the graph to obtain the largest minimum label of k and the upper bound is analyzed by labeling the vertices and edges of the graph, where the largest label is k and the values for each vertices weight is different. The result obtained for the total vertex irregularity strength of a series parallel graph  is .

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Author Biography

Aminah Utami, Mathematics Department, Islamic State University Sultan Syarif Kasim Riau, Indonesia

Department Mathematics

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Published
2024-03-01
How to Cite
[1]
C. Marzuki, A. Utami, M. Elviyenti, and Y. Muda, “ON THE TOTAL VERTEX IRREGULARITY STRENGTH OF SERIES PARALLEL GRAPH sp(m,r,4)”, BAREKENG: J. Math. & App., vol. 18, no. 1, pp. 0213-0222, Mar. 2024.
Issue
Vol 18 No 1 (2024): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2024 Corry Corazon Marzuki, Aminah Utami, Mona Elviyenti, Yuslenita Muda

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