2024/07/17 by So Hirata, Hirata, So
Computer Science · Mathematics · #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR) #Point processes and geometric inequalities #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2407.12961
openalex publication_date 2024/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 (≥ 3), even girth g (≥ 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 Bollobás and de la Vega. They range from 60% to 77% of the correct diameters of large-n graphs.