Problem Solved!
I have set in the route-eth0 file on computer A the gateway as the ip i.e 192.168.1.10
Now both are pinging without any problems.
However, can anyone provide the link which explains the routing concept clearly!
Now Final configuration files for help for future users.
Computer A's ifcfg-eth0
Code:
IPADDR=192.168.1.10
NETMASK=255.255.255.0
GATEWAY=192.168.1.254
Computer A's route-eth0 file
Code:
ADDRESS0=10.0.0.0
NETMASK0=255.255.255.0
GATEWAY0=192.168.1.10
Computer B's ifcfg-p2p1 file
Code:
IPADDR=10.0.0.10
NETMASK=255.255.255.0
GATEWAY=10.0.0.1
Computer B's route-p2p1 file
Code:
ADDRESS0=192.168.1.0
NETMASK0=255.255.255.0
GATEWAY0=10.0.0.10