Overview

CombinatoRoyal Inc. is a Research & Development (R&D) company that has been carrying out its research over the last 25 years specializing in Graph Theory and Combinatorial Optimization. CombinatoRoyal has a very thorough and expedient approach for finding Combinatorial Optimization solutions that are stored in its database for easy access and retrieval. CombinatoRoyal's expertise in Graph Theory and Graph Isomorphism has evolved to the extent where today all the Combinatorial Optimization solutions found are resolved by CombinatoRoyal's unique set of invariants. There is no "Canonization" process for resolving any of the Combinatorial Optimization solutions found. Two distinct algorithms are used in the searches, namely for t-designs and non t-designs. All the non-isomorphic designs found for any parameter, have the exact same starting "entry" point and ending "exit" point. CombinatoRoyal Inc. is committed to and envisions that in the future it will be able to simulate searches in the natural and orderly fashion that a "Brute Force Search" would be carried and as such all the solutions found would be at their Lexicographically Smallest Graph Equivalent (LSGE). A "Brute Force Search" would in essence allow for completely modular and asynchronous searches that could be distributed on different computers without synchronization. CombinatoRoyal Inc. has also created a formula that expedites the process of finding and proving the lowest bounds for any combinatorial design parameter without exceptions. The formula is continuously expandable and scalable for all V, K , t and lambda and compliments Graph Isomorphism.