Distance-regularity and the spectrum of graphs
This paper considers the question whether a graph with the spectrum of a distance regular graph is distance regular. It has been known that the answer is affirmative if the distance regular graph has diameter not greater than 2, and that the answer is negative if the diameter is greater than 3. This paper shows that the answer is negative for several distance regular graph with diameter 3, including the tetrahedral \(J(n,3)\), and that the answer is positive for diameter greater than 2, provided some additional requirement is fulfilled.
scientific article; zbMATH DE number 871270
scientific article