Fault diameter of Cartesian product graphs

The (k−1)-fault diameter Dk(G) of a k-connected graph G is the maximum diameter of G−F for any F⊂V(G) with |F|<k. Krishnamoorthy and Krishnamurthy first proposed this concept and gave Dκ(G₁)+κ(G₂)(G₁×G₂)?Dκ(G₁)(G₁)+Dκ(G₂)(G₂) when κ(G₁×G₂)=κ(G₁)+κ(G₂), where κ(G) is the connectivity of G. This paper gives a counterexample to this bound and establishes Dk₁+k₂(G₁×G₂)?Dk₁(G₁)+Dk₂(G₂)+1 for any ki-connected graph Gi and ki?1 for i=1,2.