Exploring New Cryptographical Construction of Complex Network Data

Abstract

There are famous scale-free network models and small-world network models that bare huge amounts of mass data. We have designed several password tree-spaces by small trees having the total graceful labellings such that every tree T in the password tree-space has a total graceful labelling. For exploring topological passwords consisted of graphic constructions pulsing number theory, we show edge-symmetric graphs G = 〈T, H, m〉, edge-asymmetric graphs G = 〈T, H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ,..., H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> 〉 and uniformly edge-symmetric graph G = 〈T, H, p〉 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">uni</sub> defined in this article differ from each other, these graphs can product various password tree-spaces. Since there are many labellings of graph theory related with number theory, so we can make more complicated password tree-spaces for the security of information and mass data networks.