DIMENSI METRIK GRAF HASIL OPERASI JEMBATAN DARI CATERPILLAR HOMOGEN DAN POT BUNGA DIPERUMUM

  • Gusma Hidayanti Pendidikan Matematika, FKIP, Universitas Mataram
  • Amrullah Amrullah Pendidikan Matematika, FKIP, Universitas Mataram
  • Nani Kurniati Pendidikan Matematika, FKIP, Universitas Mataram
  • Laila Hayati Pendidikan Matematika, FKIP, Universitas Mataram

Abstract

The metric dimension is a concept that has many applications, such as robotic navigation. This concept will distinguish each vertex of a graph based on some vertices. The distinguishing vertices are called the basis of the graph. Let G be a connected graph, the metric dimension, dim(G), is the smallest cardinality of the basis of graph G. On this paper, we present the metric dimensions of the bridge graph of a homogeneous caterpillar graph Cm,n and a generalized flower pot graph $C_p-K_{(q_1, q_2,\cdos,q_p}$. This research was conducted by the approach of structure analysis by location of the bridge vertices, the edge of the bridge, and the order of the graph. The results show that the metric dimensions of the bridge graph are at least can be reduced at most 2, and the maximum values are the same as the value of $m(n-1)+ \sum_{i=1}^p q_i- 2p$.
Keywords: Metric dimension, caterpillar, unicyclic, bridge
MSC2020: 05C12

Published
2022-03-24
How to Cite
HIDAYANTI, Gusma et al. DIMENSI METRIK GRAF HASIL OPERASI JEMBATAN DARI CATERPILLAR HOMOGEN DAN POT BUNGA DIPERUMUM. Majalah Ilmiah Matematika dan Statistika, [S.l.], v. 22, n. 1, p. 69-81, mar. 2022. ISSN 2722-9866. Available at: <https://jurnal.unej.ac.id/index.php/MIMS/article/view/30350>. Date accessed: 07 july 2022. doi: https://doi.org/10.19184/mims.v22i1.30350.