It is clear from the literature that a graph G has metric dimension dim(G)=1 iff G is a Path and dim(H)=2=2*dim(G) if H is a simple cycle . Can one find other pair of Graphs with similar property?. Here relation between G and H is nothing but enhancement of G.
El-Sayed Badr
There many relations as the above relation like:
dim(H)=3=3*dim(G) ( G is path graph and H is Petersen graph G(5; 2) )
dim(H)=n-1=n*dim(G) ( G is path graph and H is complete graph with n vertices)
dim(H)=2=2*dim(G) ( G is path graph and H is wheel graph (W1;4) or (W1;5) )
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etc
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