Relaxing an edge asks whether reaching a neighbor through the current router improves the known distance. This topology includes one visible improvement for E.
highlighted = computed this step
C proposes E
C reaches E with distance 7 through the C-E edge.
d(E)=7
Show the first E claim
That claim is C's final distance 2 plus edge C-E weight 5, giving 7.
2+5=7
D improves E
Later D reaches E with distance 6 through the D-E edge.
d(E)=6
Show the better E claim
The D route is D's final distance 5 plus edge D-E weight 1, giving 6.
5+1=6
Keep the smaller claim
E improves because 6 is less than 7.
6<7
Update the predecessor too
When E improves to 6, its predecessor changes to D. That predecessor is what later appears in the tree.
pred(E)=D
Summary
Relaxation replaces a tentative distance only when the new route is strictly smaller.