A strict lower bound for the diameter of a symmetric graph is proposed, which is calculable with the order $n$ and other local parameters of the graph such as the degree $k\,(\geq 3)$, even girth $g\,(\geq 4)$, and number of $g$-cycles traversing a vertex, which are easily determined by inspecting a small portion of the graph (unless the girth is large). It is applied to the symmetric Cayley graphs of some Rubik's Cube groups of various sizes and metrics, yielding slightly tighter lower bounds of the diameters than those for random $k$-regular graphs proposed by Bollob\'{a}s and de la Vega. They range from 60% to 77% of the correct diameters of large-$n$ graphs.

翻译：本文提出了一种对称图直径的严格下界估计方法，该下界可通过图的阶数$n$及其他局部参数计算得出，这些参数包括度数$k\,(\geq 3)$、偶围长$g\,(\geq 4)$以及经过某顶点的$g$-圈数量。这些参数通常只需检查图的局部结构即可确定（除非围长较大）。将该方法应用于不同规模与度量下的魔方群对称凯莱图，得到了比Bollobás和de la Vega提出的随机$k$-正则图直径下界更精确的估计结果。对于大$n$图，该下界可达实际直径的60%至77%。