A concept of ip default-gateway needs to be confirmed

Thank you for your reply. I think as layer3, ping packet always should go through routing table even if two routers connected with each other directly. I am not sure if the concept is correct

The following(config and diagram attached) is what i tested. First time it confirmed default-gateway is unnecessary, but after redid it, it confirmed the default-gateway is necessary for R8 to ping R6. I used gns to do it. it is unstable sometimes. but I believe second test.

here is what think about the issue: I think the issue should be considered like this: If an end router has only one ip address connected with other device, the router cannot be reached by user located in different network unless the router has default route. The default route in the router is like ip default-gateway in the switch that we are talking about. if anyone are interested, it could be pasted and confirm it.

-------------------------------
R6#sh run
interface FastEthernet1/0
 switchport access vlan 2
 no ip address

interface Vlan2
 ip address 67.1.1.6 255.255.255.0
 no ip proxy-arp
 no ip route-cache
--------------------------------------------

R7#sh run
interface FastEthernet1/0
 switchport access vlan 2
 no ip address
!
interface FastEthernet1/1
 no ip address
!
interface Vlan1
 ip address 1.1.1.7 255.255.255.0
 no ip proxy-arp
!
interface Vlan2
 ip address 67.1.1.7 255.255.255.0
 no ip proxy-arp
---------------------------------------------------

R8#sh run
interface FastEthernet1/0
 switchport access vlan 2
 no ip address
!
interface Vlan1
 ip address 1.1.1.8 255.255.255.0
 no ip proxy-arp
!
ip route 0.0.0.0 0.0.0.0 1.1.1.7
!
Capture.PNG

Thank you !!

Hi You are all expert! If you are interested, can you take a look at blow question, Thank you

https://www.experts-exchange.com/questions/28688006/Can-not-change-username-when-I-try-to-login-to-ASA.html

https://www.experts-exchange.com/questions/28688143/Cannot-log-in-to-failover-ASA5555-by-tacacs-username.html