Neumaier graphs with few eigenvalues
Aida Abiad, Bart De Bruyn, Jozefien D'haeseleer, Jack H. Koolen
TL;DR
This paper investigates the spectral properties of Neumaier graphs, establishing conditions for strong regularity, proving the non-existence of certain eigenvalue configurations, and classifying those with the smallest eigenvalue of -2.
Contribution
It provides new necessary and sufficient conditions for Neumaier graphs to be strongly regular and classifies those with smallest eigenvalue -2, advancing understanding of their spectral structure.
Findings
No Neumaier graphs with exactly four eigenvalues exist.
Conditions for Neumaier graphs to be strongly regular are established.
Neumaier graphs with smallest eigenvalue -2 are classified.
Abstract
A Neumaier graph is a non-complete edge-regular graph containing a regular clique. In this paper we give some sufficient and necessary conditions for a Neumaier graph to be strongly regular. Further we show that there does not exist Neumaier graphs with exactly four distinct eigenvalues. We also determine the Neumaier graphs with smallest eigenvalue -2.
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Taxonomy
TopicsFinite Group Theory Research · Coding theory and cryptography · Graph theory and applications