Abstract

The metric dimension is one of the problems in graph theory which is interesting to study until now. The metric dimension has many applications such as image processing. However, not all graphs have been obtained for the metric dimensions such as a bridge graph. A bridge graph is a graph obtained from two connected graphs , with adding a new edge where in dan in . A bridge graph is a new graph which has a larger order than the previous graph or . Therefore, the subdivision graph metric dimension can be obtained from the metric dimension before subdivision. Metric dimension of bridge graph can be determined by analysis of structure and analysis of the distance between vertices. This article shows the upper bound of a bridge graph from two connected graphs. In addition, this paper shows metric dimension the bridge graphs which obtained from the caterpillar and cycle graph.

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