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

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 C_m,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