Partition dimension of graphs with two bridges on rose graphs

Source abstract

<p>The partition dimension of a graph <em>G</em>, denoted by <em>pd</em>(<em>G</em>) is a generalization of the metric dimension, in which the distinction between vertices is no longer based on a specific set of vertices, but rather on a partition of the vertex set of the graph. A partition is called a resolving partition if every vertex in the graph has a distinct distance vector representation with respect to each subset in the partition. The minimum cardinality of such a resolving partition is called the partition dimension of the graph. This study focuses on the partition dimension of double bridge graphs constructed from a pair of rose graphs. It is shown that the partition dimension of the double bridge graph obtained from two rose graphs connected by two bridge edges is 4</p>