Algebraic Cayley graphs over finite local rings

作者：Rasri Arnisa; Meemark Yotsanan^*

来源：Finite Fields and Their Applications, 2017, 48: 227-240.

DOI：10.1016/j.ffa.2017.08.002

• Algebraic Cayley graphs
• Expander graphs
• Weil's bound

In this work, we define and study the algebraic Cayley directed graph over a finite local ring. Its vertex set is the unit group of a finite extension of a finite local ring R and its adjacency condition is that the quotient is a monic primary polynomial. We investigate its connectedness and diameter bound, and we also show that our graph is an expander graph. In addition, if a local ring has nilpotency two, then we obtain a better view of our graph from the lifting of the graph over its residue field.

• 出版日期2017-11