Research Article

# The metric dimensions of bridge graphs for some classes of graphs

@INPROCEEDINGS{10.4108/eai.12-10-2019.2296430, author={Amrullah Amrullah and Syahrul A and Turmuzi M and Baidowi Baidowi and Nani K}, title={The metric dimensions of bridge graphs for some classes of graphs}, proceedings={Proceedings of the 7th Mathematics, Science, and Computer Science Education International Seminar, MSCEIS 2019, 12 October 2019, Bandung, West Java, Indonesia}, publisher={EAI}, proceedings_a={MSCEIS}, year={2020}, month={7}, keywords={metric dimension bridge graph cycle graph complete graph star graph}, doi={10.4108/eai.12-10-2019.2296430} }

- Amrullah Amrullah

Syahrul A

Turmuzi M

Baidowi Baidowi

Nani K

Year: 2020

The metric dimensions of bridge graphs for some classes of graphs

MSCEIS

EAI

DOI: 10.4108/eai.12-10-2019.2296430

## Abstract

There are many open problems in the metric dimension of a graph, espessially the bridge graph and the disconnected graph, that have not been resolved until now. This paper presents the metrics dimension of the bridge graph in several classes of graphs namely cycle, complete, and star graphs. We know that the metric dimensions of the complete, cycle or star graph have been obtained. The bridge graph B (G1, G2, e) is a graph which is obtained from the operation of adding edge e to graphs G1 and G2. To obtain the metric dimension of the bridge graph from the graphs G1 and G2 on edge e, pd(B(G1, G2, e)), we used the graph structure of G1, G2 and the properties of the bridge graph based on the endpoint on the edge e. The results obtained the metric dimension of the bridge graph B(G1, G2, e) for the cycle, complete, or star graphs.