An application of super mean and magic graphs labeling on cryptography system

Abstract

An edge-magic total (EMT) labeling on a simple graph G with p vertices and q edges is a bijection f: V∪E→{1, 2, ..., p + q} such that for each edge xy of G, f(x) + f(xy) + f(y) = k, for a fixed positive integer k. Moreover, an EMT labeling f is a super edge-magic total labeling (SEMT) if f(V) = {1, 2, ..., p}. Furthermore, a graph G is called a super mean (SM) graph if there exists an injective function f from the vertices of G to {0,1,2,...,q} such that when each edge uv is labeled with (f(u) +f(v))/2 when f(u) +f(v) is even, and (f(u) +f(v) + 1)/2 when f(u) +f(v) is odd, then the resulting edge labels are distinct. There are two essentials results that will be proposed in this paper. In the first result, we show that a graph (n, 1) - F Caterpillar has a SM labeling and a graph Hu,y ⊙ K̄n has a SEMT labeling. In the second result, we will give an application of these labeling to increase the security level of Affine Cipher in which to encrypt a text on socials media.