Dimensi Partisi Graf Hasil Amalgamasi Sisi Graf Roda dengan Graf Bintang

Ahmad Syukur Daming; Yuliani Yuliani

doi:10.37905/euler.v12i2.27683

Dimensi Partisi Graf Hasil Amalgamasi Sisi Graf Roda dengan Graf Bintang

Ahmad Syukur Daming, Yuliani Yuliani

Abstract

This study discusses the analysis of the partition dimension of the graph resulting from the edge amalgamation between the wheel graph ( Wn) and the star graph ( Sm), where the partition dimension is an important parameter in graph theory that serves to measure the minimum number of partitions required to distinguish every pair of vertices through a set of supporting vertices. The amalgamation process is carried out by merging one edge of the wheel graph with one edge of the star graph, thus forming a new graph. This research employs theoretical and algorithmic approaches to calculate the partition dimension of the resulting amalgamated graph, focusing on the influence of the number of vertices in both constituent graphs on the changes in the partition dimension. The results show that pd(amal_s(Wn,Sm;v1v2,u1u2))=3 when 4<n<7 and m=3, and 4 when n=3 and 3≤m≤4, whereas if n≥8 and 3≤m≤⌊n/2⌋, then ⌊n/2⌋ is obtained.

Keywords

Graph;Partition dimension; Vertex amalgamation; Whell Graph; Star Graph

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References

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DOI: https://doi.org/10.37905/euler.v12i2.27683

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