The Partition Dimension on the Grid Graph
DOI:
https://doi.org/10.20956/j.v19i2.23904Keywords:
grid graph, partition dimensions, resolving partition, partition setAbstract
Graph G is a discrete set pair with the notation V(G) with its element called a vertex and the set of different and unordered pairs with the notation E(G) where the element is called edge. One type of graph Gm,n is a grid graph that is notated is a graph of the result of the operation between two path graphs (Pm*Pn). The set of partition∏ ={S1,S2,…,Sk} of V(G) is called a resolving partition if its representation for each vertex on graph G is different. The cardinality of the minimum resolving partition of graph G is the partition dimension of the graph G denoted pd(G). This paper discusses the dimension of the grid graph partition Gm,n with the result pd(Gm,n) = 3 for m,n>=2 with n even value.
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