how can we implement one-armed solution with only on vlan between F5 and our gateway router.
This can be implemented by using one VLAN and a default route in the BIGIP.
You will have to configure F5 BIGIP with self IPs in the same vlan and create a default route pointing to your router.
In case your back-end servers (pools members) in a different VLAN the F5 will reach these servers via the router. Otherwise, if your back-end servers are in the same VLAN make sure to use SNAT or make the F5 floating IP as the back-end servers Gateway.
I hope this helps.
so kindly explain what is different between one-Armed and two-Armed design
Typically, one-armed is when the communications between BIGIP and clients , and the communications between BIGIP and pools members using the same VLAN.
And two-armed is when you use defferent VLANs i.e. different self-IPs, one VLAN for the communications between BIGIP and clients , and the other VLAN for the communications between BIGIP and pools members.
I hope that helps.