Algebraic Cayley graphs over finite local rings |
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Institution: | Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok, 10330, Thailand |
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Abstract: | 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. |
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Keywords: | Algebraic Cayley graphs Expander graphs Weil's bound |
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