Majalah Ilmiah Matematika dan Statistika (MIMS)
Vol 22 No 1 (2022): Majalah Ilmiah Matematika dan Statistika

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

Hidayanti, Gusma (Unknown)
Amrullah, Amrullah (Unknown)
Kurniati, Nani (Unknown)
Hayati, Laila (Unknown)

Publish Date
24 Mar 2022

#### 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, bridgeMSC2020: 05C12

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Journal Info

Abbrev

MIMS

Publisher

Subject

Mathematics

Description

The aim of this publication is to disseminate the conceptual thoughts or ideas and research results that have been achieved in the area of mathematics and statistics. MIMS, focuses on the development areas sciences of mathematics and statistics as follows: 1. Algebra and Geometry; 2. Analysis and ...