Hello Kumar,
you are referrring to the so called U shape design where in order to have both OSI layer2 links up the two core/distribution switches are connected by a L3 link instead of an OSI layer2 trunk.
The classic design is to use core switch 1 as root bridge for half of vlans ( for example even vlans) and core switch2 as root bridge for the other half of vlans (for example odd vlans)
However, all the discussion is about how to consider the use of L2 core to core link: there can be cases where a packet destinated to a GLBP virtual forwarder has to go via the other core switch at OSI layer 2 to reach the AVF if the AVF is not associated to the root bridge for the vlan we are considering.
Some people can say we are wasting bandwidth on the core to core L2 link.
Some other people may also warry for the added delay the frame experience in going via both core switches.
In the U design an access switch points to the AVF directly using the L2 uplink towards the core switch that owns the AVF role.
At the same time traffic coming from the core regardless of what core switch is used uses the direct L2 uplink towards the appropriate access layer switch.
However, what happens if one uplink of access layer SWk fails ?
if multiple access layer switches are part of the client vlan(s) the path may go to access layer SWJ to reach other core switch at layer 2 to go on the surviving uplink to SWk.
if no other switch is part of the Vlan(s) only the other core switch will advertise the associated IP subnet.
GLBP roles of AVG and AVF1 and AVF2 will be taken by the core switch with still a connection to the switch in case of a vlan not spanning over multiple access layer switches.
So I would say it depends also on how vlans are associated to access layer switches.
Hope to help
Giuseppe