Proceedings of the 7th Mathematics, Science, and Computer Science Education International Seminar, MSCEIS 2019, 12 October 2019, Bandung, West Java, Indonesia

Research Article

The metric dimensions of bridge graphs for some classes of graphs

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  • @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
Amrullah Amrullah1,*, Syahrul A1, Turmuzi M1, Baidowi Baidowi1, Nani K1
  • 1: Mathematics Education Departement, Universitas Mataram Jln Majapahit no 62 Mataram, Indonesia
*Contact email: amrullah@unram.ac.id

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.