The metric dimensions of bridge graphs for some classes of graphs
Amrullah, Turmuzi M, Syahrul A., Baidowi, Nani K.

Universitas Mataram

Abstract

The metric dimension of a graph is one of the interesting problems in the research of dimensions of the graph. There are many open problems that have not been resolved until now, some of them are metrics dimension of the bridge graph and metrics dimension of the disconnected graph. This paper presents the metrics dimension of the bridge graph in several classes of graphs namely circle, complete, and star graphs. We know that the metric dimensions of the complete, circle or star graph have been obtained.
The bridge graph B (G_1,G_2,e) is a graph which is obtained from the operation of adding edge e to graphs G_1 and G_2. To obtain the metric dimension of the bridge graph from the graphs G_1 and G_2 on edge e, pd(B (G_1,G_2,e)), we used the graph structure of G_1, G_2 and the properties of the bridge graph based on the endpoint on the edge e. The results, we have show the metric dimension of the bridge graph B(G_1,G_2,e) for the circle, complete, or star graphs.

Keywords: metric dimension, bridge graph, circle graph, complete graph, star graph

Topic: Mathematics