simplifying an equation

simplifying an equation

I gave details here of my last question...I hope this helps
I am having doubt over an equation. That is my calculation. Can anybody
check and find the error, if any. Specially in the last line. I am
confused. Thanks a lot.
NOTE : please check only last two equations. Here I am asking whether we
can write $min\{d(g,g'),d(h,h')\}$ as $min\{ecc(g),ecc(h)\}$ where
$d(g,g')$ runs over every vertex $g \in V(G)$. We know that $ecc(g,h)$=
max{d(g,g'),d(h,h')} can be written as $max\{ecc(g),ecc(h)\}$.
Am I right in writing $min\{d(g,g'),d(h,h')\}$ as $min\{ecc(g),ecc(h)\}$.
If I am wrong please help me there. If any other details needed, please
mention that. I will do that too. We took vertex as $(g,h)$ because its a
vertex of product graph and for such graphs vertex set is the cartesian
product of $V(G)$ and $(VH)$.

http://en.wikipedia.org/wiki/Glossary_of_graph_theory