Divisible design graphs with selfloops

2025/05/06 by Anwita Bhowmik, Bhowmik, Anwita, Bart De Bruyn +3 · 1 citation
Computer Science · Engineering · #Advanced Materials and Mechanics #Combinatorics (math.CO) #FOS: Mathematics #Model-Driven Software Engineering Techniques

paper · pdf · doi:10.48550/arxiv.2505.03276

openalex publication_date 2025/05/06 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

We develop a basic theory for divisible design graphs with possible selfloops (LDDG's), and describe two infinite families of such graphs, some members of which are also classical examples of divisible design graphs without loops (DDG's). Among the described theoretical results is a discussion of the spectrum, a classification of all examples satisfying certain parameter restrictions or having at most three eigenvalues, a discussion of the structure of the improper and the disconnected examples, and a procedure called dual Seidel switching which allows to construct new examples of LDDG's from others.

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• Thin divisible designs graphs: an interplay between fixed-point free involutions of (v,k,λ)-graphs and symmetric weighing matrices

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