In this paper, we have further elaborated MPLS multicasting under the specific graph (graceful) labeling with the use of specific multicast tree topology called caterpillar, which is next higher topological structure other than the path; that is a central concept in the IP unicast routing. The use of caterpillar as the multicast tree has been analyzed and compared with the other tree topologies under the new measure of the multicast network metric. We have applied graceful label distributions to the links of the spanning caterpillars associated to the autonomous sub-networks (AN) that involved in the multicasting. The labeling algorithm proposed uniquely assigns link labels based on the node numbering which in turn enables to give a sharp estimate to the time-to-live parameter, optimal selection of RP (rendezvous points) of multicast caterpillar topology to nodes in the ANs by transmitting of 'graceful code' in the form of sequence of (n-2) node numbers. The graceful code for the caterpillar has revealed an efficient method (G-trace) of the reconstruction of multicast tree topology which in turn to be used for maintainability and for the other purposes in the management site.