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 u...

A tree with n vertices is called graceful if there exists a labeling of its vertices with the numbers from 1 to n such that the set of absolute values of the differences of the numbers assigned to the ends of each edge is the set {1, 2, .., n− 1}. The problem of whether or not all trees are graceful is still open. In this paper, we give an extensive survey of most of the results related to this...

Graceful labelings use a prominent place among difference vertex labelings. In this work we present new families of graceful graphs all of them obtained applying a general substitution result. This substitution is applied here to replace some paths with some trees with a more complex structures. Two caterpillars with the same size are said to be textit{analogous} if thelarger stable sets, in bo...

Graph labeling is an important area of research in Graph theory. There are many kinds of graph labeling such as Graceful labeling, Magic labeling, Prime labeling, and other different labeling techniques.In this paper the Prime labeling of certain classes of graphs are discussed.It is of interest to note that H-graph which is a 3 –regular graph satisfy Prime labeling. A Gear graph is a graph obt...