关于限制酉Cayley图和模n的辛变换
On restricted unitary Cayley graphs and symplectic transformations modulo n
摘要：
我们提出了一些意见的一个受限制的变种的酉凯莱图模n，和分解的元素的辛算子的整数模n的影响。定义了顶点集为环Z_n的二次酉Cayley图G_n，其中模n的剩余a，b相邻当且仅当它们的差是二次剩余.通过限定这类图的直径，我们给出了Z_n上分解一个辛矩阵所需的基本运算（辛标量乘法、辛行交换和行加减）的个数的上界.我们还刻画了n上G_n为完美图的条件。
英文摘要：
We present some observations on a restricted variant of unitary Cayley graphs modulo n, and the implications for a decomposition of elements of symplectic operators over the integers modulo n. We define quadratic unitary Cayley graphs G_n, whose vertex set is the ring Z_n, and where residues a, b modulo n are adjacent if and only if their difference is a quadratic residue. By bounding the diameter of such graphs, we show an upper bound on the number of elementary operations (symplectic scalar multiplications, symplectic row swaps, and row additions or subtractions) required to decompose a symplectic matrix over Z_n. We also characterize the conditions on n for G_n to be a perfect graph.
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