Graceful Labeling and Skolem Graceful Labeling on the U-star Graph and It’s Application in Cryptography

Abstract

Graceful Labeling on graph G=(V, E) is an injective function f from the set of the vertex V(G) to the set of numbers {0,1,2,...,|E(G)|} which induces bijective function f from the set of edges E(G) to the set of numbers {1,2,...,|E(G)|} such that for each edge uv e E(G) with u,v e V(G) in effect f(uv)=|f(u)-f(v)|. Meanwhile, the Skolem graceful labeling is a modification of the Graceful labeling. The graph has graceful labeling or Skolem graceful labeling is called graceful graph or Skolem graceful labeling graph. The graph used in this study is the U-star graph, which is denoted by U(Sn). The purpose of this research is to determine the pattern of the graceful labeling and Skolem graceful labeling on graph U(Sn) apply it to cryptography polyalphabetic cipher. The research begins by forming a graph U(Sn) and they are labeling it with graceful labeling and Skolem graceful labeling. Then, the labeling results are applied to the cryptographic polyalphabetic cipher. In this study, it is found that the U(Sn) graph is a graceful graph and a Skolem graceful graph, and the labeling pattern is obtained. Besides, the labeling results on a graph it U(Sn) can be used to form a table U(Sn) polyalphabetic cipher. The table is used as a key to encrypt messages.

Arithmetic Sequential Graceful Labeling of Star Related Graphs – II

“…Hence, f is arithmetic sequential graceful labeling and the graph B n,n 2 is arithmetic sequential graceful graph. Example 3.2: The graph B 3,3 2 and its arithmetic sequential graceful labeling are shown in Figure 1. The graph S ′ (k 1,n ) is an arithmetic sequential graceful graph.…”

“…According to a recent dynamic survey (1) of graph labeling, numerous scholars contribute their work on various forms of graceful labeling, such as Skolem Graceful Labeling, Edge Even Graceful Labeling, Odd Graceful Labeling and so on. Pasaribu M, Yundari Y, Ilyas M (2) proved that U-star graph is a graceful graph and skolem graceful graph. Zeen El Deen MR, Omar NA (3) proved that the double star graph and path related graphs are r-edge even graceful graph.…”

Arithmetic Sequential Graceful Labeling on Star Related Graphs

“…Labeling is the process of giving values to edges or vertices. According to a recent dynamic survey, (1) of graph labeling, numerous scholars contribute their work on various forms of graceful labeling, such as Skolem Graceful Labeling (2) , Edge Even Graceful Labeling (3,4) . Odd Graceful Labeling (5) , and so on.…”

Key Generation in Cryptography Using Radio Path Coloring

“…An alternative technique of employing graph labeling techniques for encryption and decryption as well as key generation is dealt by earlier researchers. [21] discussed the application of graceful labeling and skolem graceful labeling on the U −star graph in cryptography. V N Jaya Shruthy and V Maheswari published articles [22], [23] on combining various graph labeling methods with cryptography.…”