In this Paper, we see about “Graceful Graphs” and have discussed the important application of Graceful Graphs in the field of Computer Science, namely, MULTI PROTOCOL LABEL SWITCHING (MPLS) related to Networking. The MPLS technique has many useful applications in networking, for example, it can be effectively used in ATM network infrastructure, as the labeled flows can be mapped to ATM virtual circuit identifiers, and vice-versa. This feature signifies the existence of graceful labeling concept in Computer Networks via MPLS.