Regular graphs with four eigenvalues (Q1899403)

Connected regular graphs having at most three distinct eigenvalues are the complete and the strongly regular graphs. Distance-regular graphs of diameter \(d\) are generalizations of complete \((d= 1)\) and strongly regular \((d= 2)\) graphs. The present paper studies the connected regular graphs with four distinct eigenvalues. Properties and feasibility conditions of the eigenvalues are presented. The paper also gives several constructions, some characterizations, and uniqueness and nonexistence results.