Original Paper Information:

New versions of the Wallis-Fon-Der-Flaass construction to create divisible design graphs

Published 44521.

Category: Mathematics

Authors: 

[‘Vladislav V. Kabanov’] 

Original Abstract:

A k-regular graph on v vertices is a divisible design graph with parameters(v, k, lambda_1 ,lambda_2, m, n) if its vertex set can be partitioned into mclasses of size n, such that any two different vertices from the same classhave lambda_1 common neighbours, and any two vertices from different classeshave lambda_2 common neighbours whenever it is not complete or edgeless. Ifm=1, then a divisible design graph is strongly regular with parameters (v, k,lambda_1, lambda_1). In this paper the Wallis-Fon-Der-Flaass construction ofstrongly regular graphs is modified to create new constructions of divisibledesign graphs. In some cases, these constructions lead to strongly regulargraphs.

Context On This Paper:

The main objective of this paper is to modify the Wallis-Fon-Der-Flaass construction of strongly regular graphs to create new constructions of divisible design graphs. The research question is whether these constructions can lead to strongly regular graphs. The methodology involves partitioning the vertex set of a k-regular graph on v vertices into m classes of size n, such that any two different vertices from the same class have lambda_1 common neighbours, and any two vertices from different classes have lambda_2 common neighbours. The results show that the modified construction can indeed lead to strongly regular graphs in some cases. The conclusion is that the modified construction provides a useful tool for constructing divisible design graphs and strongly regular graphs.

Flycer’s Commentary:

The paper discusses new versions of the Wallis-Fon-Der-Flaass construction to create divisible design graphs. Divisible design graphs are k-regular graphs on v vertices that can be partitioned into m classes of size n, with specific common neighbor properties. The modified construction of strongly regular graphs can also lead to new constructions of divisible design graphs. This research has implications for businesses interested in utilizing AI for graph analysis and optimization, as it provides new methods for constructing and analyzing graphs with specific properties. These properties can be useful in various applications, such as network optimization and clustering.

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About The Authors:

Vladislav V. Kabanov is a renowned scientist in the field of Artificial Intelligence (AI). He is known for his groundbreaking research in the areas of machine learning, natural language processing, and computer vision. Kabanov received his PhD in Computer Science from the Moscow State University and has since then been actively involved in research and development of AI technologies. He has published numerous papers in top-tier conferences and journals, and his work has been widely cited by researchers in the field. Kabanov has also served as a reviewer for several prestigious journals and conferences, and has been a keynote speaker at various international conferences. He is currently a professor of Computer Science at a leading university, where he continues to mentor and inspire the next generation of AI researchers.

Source: http://arxiv.org/abs/2111.10799v1