Gracefulness of P - nLeggedC4- P' Graph
Sanjida Nasreen Tumpa, Md. Tasnim Manzur Ankon · 2018
Graph labeling is the concept of assigning identifiers to the nodes in a graph. The concept, being introduced in the late 1960s, has flourished much over time, and numerous papers have been written based on multiple labeling concepts. Graceful labeling, a particularly unique concept of graph labeling, was introduced by Rosa in 1967, which follows the idea that every vertex of a graph with e edges can be assigned a unique label from the set { 0, 1, 2, ..., e }, and the labels of the edges will be assigned with the absolute difference between the labels of its adjoining edges, where every edge will have a unique label. Much research has been conducted to prove more and more classes are graceful, which itself has significant application in numerous fields, like road mapping, resource distribution, radio astronomy, cryptography, traffic routing, X-ray crystallography. In this paper, we introduce a class of graph, created from a collection of path graph and C4 cycle graph, terming it as P - n Legged C4- p' graphs, and provide enough reference to prove that the derived class is graceful. We also provide mathematical expressions for every vertex in the graph, whilst considering multiple cases of path and chain length.