The main idea of this paper is to provide an algebraic algorithm for constructing symmetric graphs with optimal fault tolerance. For this purpose, we use normal edge-transitive Cayley graphs and the idea of reconstruction question posed by Praeger to present a special factorization of groups which induces a graphical decomposition of normal edge-transitive Cayley graphs to simpler normal edge-transitive Cayley graphs. Then as a consequence of our results, we continue the study of normal edge-transitive Cayley graphs of abelian groups and we show that knowing normal edge-transitive Cayley graphs of abelian p-groups, we can determine all normal edge-transitive Cayley graphs of abelian groups.

本文的主要思想是提供一种代数算法，以构建具有最佳容错能力的对称图。为此，我们使用法线边缘可导Cayley图和Praeger提出的重构问题的思想来提出特殊的基团分解，从而将法线边缘可导Cayley图分解为更简单的法线边缘可导Cayley图。然后，由于我们的研究结果，我们继续研究阿贝尔群的正态边传递Cayley图，并且表明，知道阿贝尔p-群的正态边传递Cayley图，我们可以确定所有的正态边导Cayley图。阿贝尔团体。