(1, N)-Arithmetic Labelling in Multimedia and Network Technology

Abstract

A graph G is said to be $(1, N)$-Arithmetic (where N is a positive integer) if there is a function f from the vertex set of G to $\{0,1,N,(N + 1),2N,(2N + 1),\dots,N(q-1),N(q-1) + 1\}$ in such a way that (i) f is $1-1$ (ii) f induces a bijection $f^{\ast }$ from the edge set of G to $\{1,N + 1,2N + 1,\dots,N(q-1) + 1\}$ where $f^{\ast }(uv)=|f(u)-f(v)|$. In this paper we investigate the experimental results and point out that the new image scrambling method established on $(1, N)$-Arithmetic labelling of tree can deliver a high level security owing to the strong anomaly of sorting transformation.