IP Loop Algebraic Structures of order 7, 9, 11 and 13 with labelled classes

Published: 13 December 2021| Version 2 | DOI: 10.17632/bywsggk65r.2
Majid Khan


The dataset consists of IP loop algebraic structures of order 7, 9, 11 and 13 in matrix format along with their corresponding isomorphism classes. Each row represents a unique algebraic structure (as a matrix stored in row major format) satisfying the IP loop constraints. The isomorphism class of each algebraic structure is also labelled. The isomorphism classes were verified by using Nauty [1]. IP loop of order 13 dataset contains 7853368 (~8 million) algebraic structures with 10342 unique isomorphism classes. IP loop of order 11 dataset contains 6464 algebraic structures with 49 unique isomorphism classes. IP loop of order 9 dataset contains 64 algebraic structures with 7 unique isomorphism classes. IP loop of order 7 dataset contains 4 algebraic structures with 2 unique isomorphism classes.


Steps to reproduce

The algebraic structures were enumerated by using a constraint solver (Google or-tools). The class labels were then assigned based on a customized implementation of an algorithm for isomorphism checking of algebraic structures. The class labels were later on verified by converting the algebraic structures into graph format and using NAUTY to test for isomorphism


Prince Mohammad Bin Fahd University


Group Theory, Graph Theory, Abstract Algebra