Quartic simple graph counts, n = 27–50

This archive provides the source code, orchestration scripts, and exact integer data used for the enumeration of simple 4-regular (quartic) graphs for orders (n=27)–(50). The src/ directory contains the PARI/GP implementation of the permutation-fixed counting recurrence based on Burnside averaging and permutation-cycle aggregation. The scripts/ directory provides standalone Python and shell utilities for preparing cycle-type tasks, executing independent fixed-point calculations, aggregating the Burnside sum, and checking the resulting integer sequences. The data/ directory contains the permutation-fixed counts and derived sequences of all unlabeled, connected unlabeled, disconnected unlabeled, and labeled simple 4-regular graphs. The deposited data extend the computation of quartic graph counts to order 50. All numerical values are stored as exact decimal integers. The archive contains counts only and does not include graph representatives. The software uses exact integer arithmetic and is designed so that fixed-point calculations for different permutation cycle types can be executed independently and in parallel. The accompanying scripts also perform consistency checks including partition coverage, conjugacy-class weights, integrality of Burnside averages, labeled identity-permutation counts, and Euler-transform consistency between unrestricted and connected graph counts. Large-order calculations may require substantial computational resources. The deposited scripts and source code are intended to support reproduction, independent checking, and further extension of the enumeration.