05526253

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05526253 Chen, Yu Chen, Baoxing Xie, Xiaohua Optimal designs of Abelian Cayley digraphs with degree 2. J. Zhangzhou Norm. Univ., Nat. Sci. 20, No. 4, 15-20 (2007). 2007 Editorial Department of Journal of Zhangzhou Normal University, Zhangzhoum Fujian EN Cayley digraph diameter Abelian group Summary: Let $G$ be a finite Abelian group with a two element generating set $M$. We consider the Cayley digraph $D(G, M)$ in which the vertices are corresponding to the elements of $G$ and there is an arc from $x$ to $y$ if and only if $y-x \in M$. An attention deserving problem is: for a given positive integer $N$, what is the minimum value of the diameters among all such connected Cayley digraphs on $N$ vertices of finite Abelian groups with degree 2? In this paper, a fast algorithm is given to compute this minimum value, and with our algorithm, we can find an Abelian Cayley digraph with degree 2 whose diameter is minimal.